# Quiz 9: Rotation

Physics & Astronomy

Q 1Q 1

Two points, A and B, are on a disk that rotates about an axis. Point A is closer to the axis than point B. Which of the following is not true?
A) Point B has the greater speed.
B) Point A has the lesser centripetal acceleration.
C) Points A and B have the same angular acceleration.
D) Point B has the greater angular speed.
E) Point A has the lesser tangential acceleration.

Free

Multiple Choice

D

Q 2Q 2

Two points, A and B, are on a disk that rotates about an axis. Point A is three times as far from the axis as point B. If the speed of point B is v, then what is the speed of point A?
A) v
B) 3v
C) v/3
D) 9v
E) v/9

Free

Multiple Choice

B

Q 3Q 3

Two objects, m

_{1}and m_{2}, both of mass m, are place on a horizontal platform which is rotating at a constant angular velocity. m_{1}= m is located at a distance R from the axis of rotation and the second object of mass m_{2}= 2m is located at a distance 2R. The angular velocity of mass m_{1}____ to the angular velocity of m_{2}. A) is less than B) is equal to C) is greater than D) depends how fast it is rotating E) unable to tellFree

Multiple Choice

B

Q 4Q 4

Two objects, m

_{1}and m_{2}, both of mass m, are place on a horizontal platform which is rotating at a constant angular velocity. m_{1}is located at a distance R from the axis of rotation and m_{2}is located at a R. The centripetal acceleration of mass m_{1}____ to the centripetal acceleration of m_{2}. A) is less than B) is equal to C) is greater than D) depends how fast it is rotating E) unable to tellFree

Multiple Choice

Q 5Q 5

Two objects, m

_{1}and m_{2}, both of mass m, are placed on a horizontal platform which is rotating at a constant angular velocity. m_{1}is located at a distance R from the axis of rotation and m_{2}is located at a R. The tangential acceleration of mass m_{1}____ to the tangential acceleration of m_{2}. A) is less than B) is equal to C) is greater than D) depends how fast it is rotating E) unable to tellFree

Multiple Choice

Q 6Q 6

Starting from rest, a disk rotates with constant angular acceleration. If it takes 10 rev to reach an angular velocity , then how many additional revolutions are required to reach an angular velocity 2?
A) 10 rev
B) 20 rev
C) 30 rev
D) 40 rev
E) 50 rev

Free

Multiple Choice

Q 7Q 7

The London Eye, which is a giant Ferris wheel, has a diameter of 135 m. It revolves at a constant rate and takes 30 minutes to complete one revolution. What is the linear velocity of a rider in a capsule that is located at the perimeter of the wheel?
A) 0.24 m/s
B) 0.47 m/s
C) 3.5 m/s
D) 7.1 m/s
E) None of the above

Free

Multiple Choice

Q 8Q 8

A record turntable rotates through 5.0 rad in 2.8 s as it is accelerated uniformly from rest. What is the angular velocity at the end of that time?
A) 0.60 rad/s
B) 0.90 rad/s
C) 1.8 rad/s
D) 3.6 rad/s
E) 14 rad/s

Free

Multiple Choice

Q 9Q 9

You have a friend who lives in the southern part of the United States, and you live in the northern part. As Earth rotates, your linear velocity is ___________ hers, and your angular velocity is ____________ hers.
A) greater than; equal to
B) equal to; greater than
C) greater than; less than
D) less than; greater than
E) less than; equal to

Free

Multiple Choice

Q 10Q 10

A wheel rotates through 6.0 rad in 2.0 s as it is uniformly brought to rest. The initial angular velocity of the wheel before braking began was
A) 0.60 rad/s
B) 0.90 rad/s
C) 1.8 rad/s
D) 6.0 rad/s
E) 7.2 rad/s

Free

Multiple Choice

Q 11Q 11

You are whirling a stone on the end of a string in a horizontal circle of radius
R = 0.65m with a frequency of 4 rev/s when the string breaks. Just after the string breaks, the velocity of the stone is
A) straight down.
B) 32 m/s along a tangent to the circle.
C) 16 m/s along the radius away from the center.
D) 1.0 m/s along the radius toward the center.
E) none of these

Free

Multiple Choice

Q 12Q 12

You are pedaling a bicycle at 9.8 m/s. The radius of the wheels of the bicycle is
51)9cm. The angular velocity of rotation of the wheels is
A) 19 rad/s
B) 2.5 rad/s
C) 4.5 rad/s
D) 3.0 rad/s
E) 6.3 rad/s

Free

Multiple Choice

Q 13Q 13

The Empire's space station is a long way from any star. It is circular and has a radius of 5.10 km. The angular velocity that is needed to give the station an artificial gravity of 9.80 m/s

^{2}at its circumference is A) 4.4 10^{-2}rad/s B) 7.0 10^{-3}rad/s C) 0.28 rad/s D) - 0.22 rad/s E) 1.3 10^{3}rad/sFree

Multiple Choice

Q 14Q 14

A wheel is rotating at 30 rev/min. The angular velocity of the wheel is
A) 2

^{2}rad/s B) 2 rad/s C) 2 rad/s D) /2 rad/s E) rad/sFree

Multiple Choice

Q 15Q 15

A particle moves uniformly around the circumference of a circle whose radius is 8.0 cm with a period of /20 s. The angular velocity of the particle is
A) 2.5 rad/s
B) 3.2 10

^{2}rad/s C) 40 rad/s D) 7.9 rad/s E) 0.96 rad/sFree

Multiple Choice

Q 16Q 16

A particle is moving uniformly in a circle of radius 50 cm. Its angular velocity is 96 rad/s. The linear speed of the particle is
A) 1.0 m/s
B) 96 cm/s
C) 48 m/s
D) zero
E) 15 m/s

Free

Multiple Choice

Q 17Q 17

A point P is at a distance R from the axis of rotation of a rigid body. The linear speed, centripetal acceleration, and tangential acceleration of the point can be expressed as
Linear
Centripetal
Tangential
Speed
Acceleration
Acceleration
A)
R
R

^{2}R B) R R R^{2}C) R^{2}R R D) R R^{2}R E) R^{2}R R^{2}Free

Multiple Choice

Q 18Q 18

A body that moves with a constant speed in a circle
A) experiences no acceleration.
B) undergoes no change in velocity.
C) has no resultant force acting on it.
D) has no work done on it.
E) is described by all of these.

Free

Multiple Choice

Q 19Q 19

When an object is moving in a circle at constant speed, its acceleration is
A) constantly increasing.
B) constant in direction.
C) zero.
D) constant in magnitude.
E) constant in both magnitude and direction.

Free

Multiple Choice

Q 20Q 20

A wheel rotates with a constant nonzero angular acceleration. Which of the following quantities remains constant in magnitude?
A) , tangential velocity
B)

_{r}, radial acceleration C)_{t}, tangential acceleration D) , angular velocity E) All of these are correct.Free

Multiple Choice

Q 21Q 21

A turntable rotating at 8.0 rad/s slows to a stop in 10 s. If the acceleration is constant, the angle through which the turntable rotates in the 10 s is
A) 0.80 rad
B) 0.40 rad
C) 40 rad
D) 80 rad
E) 16 rad

Free

Multiple Choice

Q 22Q 22

What physical quantity is represented by the slope of the curve shown on the graph?
A) displacement
B) angular acceleration
C) tangential acceleration
D) velocity
E) None of these is correct.

Free

Multiple Choice

Q 23Q 23

You give an orbiting satellite a command to rotate through an angle given by
= at + bt

^{2}- ct^{4}Where a, b, and c are constants and is in radians if t is in seconds. What is the angular acceleration of this satellite at time t? A) at B) a + b - c C) -12 D) 2b - 12ct^{2 }E) zeroFree

Multiple Choice

Q 24Q 24

The angular acceleration of the flywheel of a generator is given by
(t) = 6bt - 12ct

^{2}Where b and c are constants and is in rad/s^{2}provided t is in seconds. If the initial angular velocity is taken to be _{0}, the angular velocity at time t is given by A) _{0}+ 6bt^{2}- 12ct^{3 }B) 6b - 24ct C) 3bt^{2}- 4ct^{3}+ _{0 }D) 3bt^{2}- 4ct^{3 }E) 6b - 24ct + _{0 }Free

Multiple Choice

Q 25Q 25

The data used to construct the graph were taken from the tachometer of an airplane. The angular acceleration during the 10 s interval was
A) 3.0 rad/s

^{2 }B) 6.0 rad/s^{2 }C) 8.0 rad/s^{2 }D) 20 rad/s^{2 }E) 38 rad/s^{2 }Free

Multiple Choice

Q 26Q 26

Which of the following statements about the motion of the second hand of a clock is true?
A) The tangential velocity of the tip is constant.
B) The angular velocity is zero.
C) The angular acceleration is zero.
D) The radial acceleration is zero.
E) The tangential acceleration is nonzero.

Free

Multiple Choice

Q 27Q 27

A turntable has an angular velocity of 1.4 rad/s. The coefficient of static friction between the turntable and a block placed on it is 0.20. The maximum distance from the center of the turntable that the block can be placed without sliding is approximately
A) 0.50 m
B) 1.0 m
C) 1.4 m
D) 2.0 m
E) 4.4 m

Free

Multiple Choice

Q 28Q 28

A penny is placed 0.10 m from the center of a turntable. If the coefficient of static friction between the penny and the turntable is 0.50, the maximum linear speed at which the penny can travel without slipping is approximately
A) 0.49 m/s
B) 0.70 m/s
C) 1.3 m/s
D) 1.4 m/s
E) 0.20 km/s

Free

Multiple Choice

Q 29Q 29

A 2.0-kg mass is attached to the end of a 5.0-m rope. The mass moves in a circular path on a horizontal frictionless surface. If the breaking strength of the rope is 40 N, the maximum translational speed with which you can swing the mass without breaking the rope is approximately
A) 3.2 m/s
B) 4.0 m/s
C) 10 m/s
D) 20 m/s
E) 0.20 km/s

Free

Multiple Choice

Q 30Q 30

A 2-kg sphere attached to an axle by a spring is displaced from its rest position to a radius of 20 cm from the axle centerline by a standard mass of 20 kg, as in Figure 1. The same 2-kg sphere is also displaced 20 cm from the axle centerline, as in Figure 2, when the sphere is rotated at a speed of approximately
A) 4.4 m/s
B) 9.8 m/s
C) 14 m/s
D) 98 m/s
E) 0.44 km/s

Free

Multiple Choice

Q 31Q 31

The ball shown in the figure will loop-the-loop if it starts from a point high enough on the incline. When the ball is at point A, the centripetal force on it is best represented by which of the following vectors?
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 32Q 32

A 5 10

^{-6}-kg dot of paint on the side of a rotating cylinder flies off when the angular speed of the cylinder reaches 5 10^{3}rad/s. The spin axis of the cylinder is vertical and its radius is 0.04 m. The force of adhesion between the paint and the surface is approximately A) 1 N B) 1 mN C) 5 mN D) 5 kN E) 5 NFree

Multiple Choice

Q 33Q 33

A 0.3-kg object is being whirled in a horizontal circle at the end of a 1.5 m long string. If the string breaks when the number of revolutions per minute, rpm = 200, then find the maximum tension in the string.
A) 2.0 10

^{2}N B) 59 N C) 7.0 10^{5}N D) 9.0 N E) 88 NFree

Multiple Choice

Q 34Q 34

A wheel starting from rest has a constant angular acceleration. After 3.0 s the angular velocity of the wheel is 7.5 rad/s. This same angular acceleration continues for a further 7.0 s after which it drops suddenly to zero. In the first 20.0 s how many revolutions does the wheel make?
A) 20
B) 40
C) 60
D) 80
E) 100

Free

Multiple Choice

Q 35Q 35

The time period for the rotation of the conical pendulum moving in a horizontal circle (bob mass = M, string length L, and vertical half angle ; see figure) is given by the expression:
A) 2 {Lcos /g}

^{1/2 }B) 2 {Lsin /g}^{1/2 }C) 2 Lcos /g D) 2 Lsin /g E) {2 Lcos /g}^{1/2 }Free

Multiple Choice

Q 36Q 36

The Crab Pulsar rotates 30 times per second. However, its period is increasing by about 10

^{}^{5}s per year. How many years will it take before its period of rotation has doubled? A) 3.0 10^{6}yr B) 6.7 10^{3}yr C) 3.3 10^{3}yr D) 1.05 10^{10}yr E) 2.10 10^{10}yrFree

Multiple Choice

Q 37Q 37

The information on a compact disc is scanned by a laser initially at a radius of 2.4 cm and then out to a maximum of 6.0 cm. Because the dimensions of the pit information remains constant with radius the disk motor adjusts so that the tangential velocity remains a constant. What is the ratio of the inner to outer rotational frequencies?
A) 0.16
B) 6.3
C) 1.0
D) 2.5
E) 0.40

Free

Multiple Choice

Q 38Q 38

A serious audiophile prefers to listen to music on his vinyl record turntable. The 12-inch diameter disk rotates at a constant 33 rpm. How fast is the record passing by the pickup cartridge tip at a radius of 4 inches? (1 inch = 2.54 cm)
A) 5.6 cm/s
B) 35 cm/s
C) 3.3 10

^{2}cm/s D) 21 m/s E) 18 cm/sFree

Multiple Choice

Q 39Q 39

In a fast rotating atomic nucleus the rate of rotation is related to the energy of the emitted gamma-ray according to the relationship "E

_{gam}_{ma}= 2hf," where h = Planck's constant, and f = rotational frequency. Find the period of rotation that corresponds to an energy of 0.75 MeV. A) 1.2 10^{}^{14}s B) 2.4 10^{}^{20}s C) 8.5 10^{19}s D) 1.7 10^{20}s E) 1.2 10^{}^{20}sFree

Multiple Choice

Q 40Q 40

A solid sphere (I = 0.4MR

^{2}) of radius 0.06 m and mass 0.50 kg rolls without slipping 14m down a 30º inclined plane. At the bottom of the plane, the linear velocity of the center of mass of the sphere is approximately A) 3.5 m/s B) 3.9 m/s C) 8.7 m/s D) 18 m/s E) 9.9 m/sFree

Multiple Choice

Q 41Q 41

Power can be expressed as the product of
A) force and displacement.
B) torque and angular displacement.
C) torque and angular acceleration.
D) force and acceleration.
E) torque and angular velocity.

Free

Multiple Choice

Q 42Q 42

A cylinder (I = ½mR

^{2}) rolls along a level floor with a speed v. The work required to stop this cylinder is A) ¼ mv^{2 }B) ½ mv^{2 }C) ¾ mv^{2 }D) mv^{2 }E) 1.25mv^{2 }Free

Multiple Choice

Q 43Q 43

The moment of inertia of a certain cylinder, whose mass is not distributed uniformly, is 0.6mR

^{2}about its geometric axis. The translational speed of the center of mass after it starts from rest and rolls 14 m down a 30º incline is approximately A) 9.3 m/s B) 86 m/s C) 13 m/s D) 3.1 m/s E) 41 m/sFree

Multiple Choice

Q 44Q 44

A solid sphere of radius r = 5 cm and mass m = 0.2 kg rolls in a groove as shown. The angle, , between the points of contact with the groove is 120. If the sphere has a linear velocity of 10 mm/s, what is the rotational kinetic energy?
A) 0.8 mJ
B) 1.0 mJ
B) 1.6 mJ
D) 2.0 mJ
E) undetermined.

Free

Multiple Choice

Q 45Q 45

The disc brakes of a high performance car are often made of carbon fiber instead of iron, thereby reducing the mass. If both types of discs are of the same size and shape, and each iron disc has a mass of 4 kg and each carbon disc has a mass of 1 kg, what is the reduction in rotational kinetic energy at 72 km/h if all the four iron discs in the car are replaced with carbon discs?
A) 300 J
B) 400 J
C) 800 J
D) 1200 J
E) 1600 J

Free

Multiple Choice

Q 46Q 46

The amount of work done on a rotating body can be expressed in terms of the product of
A) force and lever arm.
B) torque and angular velocity.
C) torque and angular acceleration.
D) force and time of application of the force.
E) torque and angular displacement.

Free

Multiple Choice

Q 47Q 47

A body of mass m is whirled at a constant angular velocity on the end of a string of length R. To double the kinetic energy of the body as it whirls while maintaining the angular velocity, the length of the string must be changed to
A) 2R
B)
C) R/2
D) 4R
E)

Free

Multiple Choice

Q 48Q 48

A ball of mass m

_{1}, connected to another mass m_{2}by a string, is whirled at a constant speed in a horizontal circle of radius R equal to 0.800m. If the mass m_{2}= 5.00 kg, the kinetic energy of the ball is A) 0.981 J B) 2.45 J C) 4.90 J D) 19.6 J E) 39.2 JFree

Multiple Choice

Q 49Q 49

A hoop of mass 50 kg rolls without slipping. If the center-of-mass of the hoop has a translational speed of 4.0 m/s, the total kinetic energy of the hoop is
A) 0.20 kJ
B) 0.40 kJ
C) 1.1 kJ
D) 3.9 kJ
E) None of these is correct.

Free

Multiple Choice

Q 50Q 50

A thin solid disk of radius R = 0.5 m and mass M = 2.0 kg is rolling without slipping on a horizontal surface with a linear speed v = 5.0 m/s. The disk now rolls without slipping up an inclined plane that is at an angle of 60 degrees to the vertical. Calculate the maximum height that the disk rolls up the incline.
A) 5.1 m
B) 2.6 m
C) 2.9 m
D) 3.1 m
E) 1.3 m

Free

Multiple Choice

Q 51Q 51

A spherical shell and a solid sphere (both of the same total mass) are rotating about a diameter at the same angular frequency and with the same rotational kinetic energy. What is the ratio of the spherical shell radius to the solid sphere (i.e., R

_{spherical shell}/R_{solid sphere})? A) (2/5)^{1/2 }B) (3/10)^{1/2 }C) (1/2)^{1/2 }D) (3/5)^{1/2 }E) (2/3)^{1/2 }Free

Multiple Choice

Q 52Q 52

Four 50-g point masses are at the corners of a square with 20-cm sides. What is the moment of inertia of this system about an axis perpendicular to the plane of the square and passing through its center?
A) 1.0 10

^{-3}kg · m^{2 }B) 4.0 10^{-3}kg · m^{2 }C) 2.0 10^{-3}kg · m^{2 }D) 8.0 10^{-3}kg · m^{2 }E) 2.8 10^{-3}kg · m^{2 }Free

Multiple Choice

Q 53Q 53

The moment of inertia of a slim rod of mass m and length L about a transverse axis through one end is mL

^{2}/3. The moment of inertia of such a rod about a transverse axis through the rod at a distance L/3 from one end is A) mL^{2}/36 B) 7mL^{2}/36 C) mL^{2}/9 D) 2mL^{2}/9 E) 4mL^{2}/9Free

Multiple Choice

Q 54Q 54

A wagon wheel consists of 8 spokes of uniform diameter, each of mass m

_{s}and length L cm. The outer ring has a mass m_{ring}. What is the moment of inertia of the wheel? Assume that each spoke extends from the center to the other ring and the ring is of negligible thickness. A) B) C) D) E)Free

Multiple Choice

Q 55Q 55

The disc brake of a high performance car is often made of carbon fiber instead of iron, thereby reducing the mass. If the mass of a carbon disc is that of iron for the same shape and size, by what factor is the moment of inertia changed?
A) one quarter
B) half
C) unchanged
D) doubled
E) quadrupled

Free

Multiple Choice

Q 56Q 56

The moment of inertia of a slim rod about a transverse axis through one end is mL

^{2}/3, where m is the mass of the rod and L is its length. The moment of inertia of a 0.24-kg meterstick about a transverse axis through its center is A) 0.14 kg · m^{2 }B) 20 kg · m^{2 }C) 0.020 kg · m^{2 }D) 80 kg · m^{2 }E) 4.5 kg · m^{2 }Free

Multiple Choice

Q 57Q 57

The moment of inertia of a set of dumbbells, considered as two mass points m separated by a distance 2L about the axis AA, is
A) mL

^{2 }B) mL^{2 }C) 2mL^{2 }D) mL^{2 }E) 4mL^{2 }Free

Multiple Choice

Q 58Q 58

A homogeneous solid cylinder of mass m, length L, and radius R rotates about an axis through point P, which is parallel to the cylinder axis. If the moment of inertia about the cylinder axis is mR

^{2}, the moment of inertia about the axis through P is A) 0.4mR^{2 }B) mR^{2 }C) 2/3 mR^{2 }D) mR^{2 }E) 1.5mR^{2 }Free

Multiple Choice

Q 59Q 59

To increase the moment of inertia of a body about an axis, you must
A) increase the angular acceleration.
B) increase the angular velocity.
C) decrease the angular velocity.
D) make the body occupy less space.
E) place part of the body farther from the axis.

Free

Multiple Choice

Q 60Q 60

If all of the objects illustrated in the figure have equal masses, the moment of inertia about the indicated axis is largest for the
A) ring
B) cross
C) sphere
D) cube
E) rod

Free

Multiple Choice

Q 61Q 61

In the figure, R

_{1}= R_{2}and cm is the center of mass. The rotational inertia about an axis through point P_{1}is I_{1}, the rotational inertia about an axis through point P_{2}is I_{2}, and the rotational inertia about an axis through the cm is I_{cm}. The relationship among the moments is A) I_{1}= I_{2}> I_{cm }B) I_{1}= I_{2}< I_{cm }C) I_{1}> I_{2}> I_{cm }D) I_{1}< I_{cm}> I_{2 }E) I_{1}= I_{2}= I_{cm }Free

Multiple Choice

Q 62Q 62

A 7.00-kg mass and a 4.00-kg mass are mounted on a spindle free to turn about the x axis as shown. Assume the mass of the arms and the spindle to be negligible. The rotational inertia of this system is approximately
A) 44.0 kg · m

^{2 }B) 47.0 kg · m^{2 }C) 99.0 kg · m^{2 }D) 148 kg · m^{2 }E) 211 kg · m^{2 }Free

Multiple Choice

Q 63Q 63

The rotational inertia of an object about an axis depends on the
A) angular velocity about the axis.
B) angular acceleration about the axis.
C) mass distribution about the axis.
D) torque about the axis.
E) linear acceleration about the axis.

Free

Multiple Choice

Q 64Q 64

A stone of mass 10 kg has a rotational inertia of 2.4 kg · m

^{2}about an axis A parallel to an axis through the center of mass. If axis A is 0)20m from the center of mass axis, the rotational inertia about the center of mass axis is A) 0.40 kg · m^{2 }B) 2.0 kg · m^{2 }C) 2.4 kg · m^{2 }D) 2.8 kg · m^{2 }E) 4.4 kg · m^{2 }Free

Multiple Choice

Q 65Q 65

A uniform disk (I

_{o}= ½ mR^{2}) of mass m and radius R is suspended from a point on its rim. The moment of inertia of the disk about an axis perpendicular to the disk through the pivot point is A) ½ mR^{2 }B) mR^{2 }C) 1.5mR^{2 }D) 2mR^{2 }E) 2mR^{2}/3Free

Multiple Choice

Q 66Q 66

A solid uniform sphere has a density of 3000 kg/m

^{3 }when the radius is equal to 0.6 m. If the mass stayed the same but the radius tripled in size, what would the new moment of inertia be for the sphere? A) 98.0 kg.m^{2 }B) 879 kg.m^{2 }C) 294 kg.m^{2 }D) 196 kg.m^{2 }E) 2650 kg.m^{2 }Free

Multiple Choice

Q 67Q 67

A disk with a radius of 1.5 m whose moment of inertia is 34 kg · m

^{2}is caused to rotate by a force of 160 N tangent to the circumference. The angular acceleration of the disk is approximately A) 0.14 rad/s^{2 }B) 0.23 rad/s^{2 }C) 4.4 rad/s^{2 }D) 7.1 rad/s^{2 }E) 23 rad/s^{2 }Free

Multiple Choice

Q 68Q 68

Two small masses, m

_{A}= 4.0 10^{-3}kg and m_{B}= 2.0 10^{-3}kg, are connected by a 1.0-m rod of negligible mass. The angular acceleration about B produced by a force of 0.016 N applied at A is approximately A) 4.0 rad/s^{2 }B) 2.7 rad/s^{2 }C) 11 rad/s^{2 }D) 12 rad/s^{2 }E) 4.0 10^{2}rad/s^{2 }Free

Multiple Choice

Q 69Q 69

A disc is free to rotate about an axis. A force applied at a distance d from the axis causes an angular acceleration . What angular acceleration is produced if the same force is applied a distance 2d from the axis?
A)
B) 2
C) /2
D) 4
E) /4

Free

Multiple Choice

Q 70Q 70

A bicycle wheel, a hollow sphere, and a solid sphere each have the same mass and radius. They each rotate about an axis through their centers. Which has the greatest moment of inertia and which has the least?
A) The wheel has the greatest; the solid sphere has the least.
B) The wheel has the greatest; the hollow sphere has the least.
C) The hollow sphere has the greatest; the solid sphere has the least.
D) The hollow sphere has the greatest; the wheel has the least.
E) The solid sphere has the greatest; the hollow sphere has the least.

Free

Multiple Choice

Q 71Q 71

Water is drawn from a well in a bucket tied to the end of a rope whose other end wraps around a cylinder of mass 50 kg and diameter 25 cm. As you turn this cylinder with a crank, the rope raises the bucket. If the mass of a bucket of water is 20 kg, what torque must you apply to the crank to raise the bucket of water at a constant speed?
A) 24 N · m
B) 2.5 N · m
C) 80 N · m
D) 2.4 10

^{3}N · m E) 49 N · mFree

Multiple Choice

Q 72Q 72

Water is drawn from a well in a bucket tied to the end of a rope whose other end wraps around a solid cylinder of mass 50 kg and diameter 25 cm. As this cylinder is turned with a crank, the rope raises the bucket. The mass of a bucket of water is 20 kg. Someone cranks the bucket up and then lets go of the crank, and the bucket of water falls down to the bottom of the well. Without friction or air resistance, what is the angular acceleration of the 50-kg cylinder?
A) 1.1 10

^{2}rad/s^{2 }B) 3.6 rad/s^{2 }C) 35 rad/s^{2 }D) 63 rad/s^{2 }E) 17 rad/s^{2 }Free

Multiple Choice

Q 73Q 73

A disc-shaped grindstone of mass 3.0 kg and radius 8.0 cm is spinning at 600 rev/min. After the power is shut off, a man continues to sharpen his axe by holding it against the grindstone until it stops 10 s later. What is the average torque exerted by the axe on the grindstone?
A) 9.6 mN · m
B) 0.12 N · m
C) 0.75 N · m
D) 0.60 kN · m
E) 0.060 N · m

Free

Multiple Choice

Q 74Q 74

A uniform stick 1 m long is placed horizontally on the ground along an east-west axis. A force of 1.0 N is applied to the center of the stick in a direction 30º west of north. The torque exerted by the force relative to the east end of the stick is
A) zero.
B) 0.25 m, clockwise.
C) 0.43 m, clockwise.
D) 0.25 m, counterclockwise.
E) 0.43 m, counterclockwise.

Free

Multiple Choice

Q 75Q 75

What constant torque, in the absence of friction, must be applied to a wheel to give it an angular velocity of 50 rad/s if it starts from rest and is accelerated for 10 s? The moment of inertia of the wheel about its axle is 9.0 kg · m

^{2}. A) 4.5 N · m B) 9.0 N · m C) 45 N · m D) 30 N · m E) 60 N · mFree

Multiple Choice

Q 76Q 76

A wheel slows from 20 rad/s to 12 rad/s in 5 s under the influence of a constant frictional torque. In these 5 s, the wheel turns through an angle of
A) 2.4 rad
B) 43 rad
C) 60 rad
D) 80 rad
E) 100 rad

Free

Multiple Choice

Q 77Q 77

A solid cylinder has a moment of inertia of 2 kg · m

^{2}. It is at rest at time zero when a net torque given by 6t^{2}+ 6 (SI units) Is applied. After 2 s, the angular velocity of the cylinder will be A) 3.0 rad/s B) 12 rad/s C) 14 rad/s D) 24 rad/s E) 28 rad/sFree

Multiple Choice

Q 78Q 78

A 7.00-kg mass and a 4.00-kg mass are mounted on a spindle that is free to turn about the x axis as shown. Assume the mass of the arms and the spindle to be negligible. The magnitude of the resultant torque is approximately
A) 82.2 N · m
B) 157 N · m
C) 225 N · m
D) 392 N · m
E) 461 N · m

Free

Multiple Choice

Q 79Q 79

A solid disk (I = MR

^{2}) that is 10 cm in diameter has a mass of 4 kg. The force applied at the outer surface required to produce an angular acceleration of 6 rad/s^{2}about an axis through the center of the disc is A) 0.24 kN B) 0.12 kN C) 0.30 N D) 0.60 N E) 1.2 NFree

Multiple Choice

Q 80Q 80

Torque is defined as
A) a force tending to cause rotation.
B) the cross product of force and displacement.
C) the product of the force and the angular displacement.
D) the product of the force and the angular velocity.
E) the rotational work done.

Free

Multiple Choice

Q 81Q 81

A thin, massless string is wrapped around a 0.25m radius grindstone supported by bearings that produce negligible frictional torque. A steady tension of 20 N in the string causes the grindstone to move from rest to a speed of 60 rad/s in 12s. The moment of inertia of the grindstone is
A) 1.0 kg · m

^{2 }B) 2.0 kg · m^{2 }C) 3.0 kg · m^{2 }D) 4.0 kg · m^{2 }E) 5.0 kg · m^{2 }Free

Multiple Choice

Q 82Q 82

The torque exerted on a perfectly spherical satellite by the gravitational pull of the sun is
A) zero.
B) directed along Earth's axis to the north pole.
C) directed along Earth's axis to the south pole.
D) in the direction of Earth's orbit.
E) directed toward the sun.

Free

Multiple Choice

Q 83Q 83

The diagrams above show the application of a force to a level arm. The arms are of the same length and = 30. Which diagram has the largest (magnitude) torque about the hinge?
A) a
B) b
C) c
D) d
E) they are the same

Free

Multiple Choice

Q 84Q 84

The diagrams above show the application of a force to a level arm. Which diagram has the largest (magnitude) torque about the hinge?
A) a
B) b
C) c
D) they are the same
E) unable to determine

Free

Multiple Choice

Q 85Q 85

A cord attached to a 3.63-kg mass is wrapped around a wheel of radius 0.610 m and released. The moment of inertia of the wheel is 2.71 kg · m

^{2}. If the wheel rotates on frictionless bearings, the acceleration of the falling weight is A) 3.26 m/s^{2 }B) 1.04 m/s^{2 }C) 2.44 m/s^{2 }D) 1.95 m/s^{2 }E) 4.27 m/s^{2 }Free

Multiple Choice

Q 86Q 86

Two masses M and m (M > m) are hung over a disc (I

_{dis}_{c}= M'R^{2}) and are released so that they accelerate. If T_{1}is the tension in the cord on the left and T_{2}is the tension in the cord on the right, then A) T_{1}= T_{2 }B) T_{2}> T_{1 }C) T_{2}< T_{1 }D) T_{2}= Mg E) T_{2}= Mg/mFree

Multiple Choice

Q 87Q 87

In a laboratory experiment, various torques are applied to a rotor and the angular acceleration is measured. The results are plotted on the accompanying graph. From the graph, the moment of inertia of the rotor is
A) 0.010 kg · m

^{2 }B) 0.011 kg · m^{2 }C) 0.0125 kg · m^{2 }D) 0.0138 kg · m^{2 }E) 0.0225 kg · m^{2 }Free

Multiple Choice

Q 88Q 88

A wheel of radius R

_{1}has an axle of radius R_{2}= R_{1}. If a force F_{1}is applied tangent to the wheel, a force F_{2}, applied tangent to the axle that will keep the wheel from turning, is equal to A) F_{1}/4 B) F_{1 }C) 4F_{1 }D) 16F_{1 }E) F_{1}/16Free

Multiple Choice

Q 89Q 89

The moment of inertia of the wheel in the figure is 0.50 kg · m

^{2}, and the bearing is frictionless. The acceleration of the 15-kg mass is approximately A) 9.8 m/s^{2 }B) 8.7 m/s^{2 }C) 74 m/s^{2 }D) 16 m/s^{2 }E) 0.53 m/s^{2 }Free

Multiple Choice

Q 90Q 90

The torque exerted on a perfectly spherical orbiting communications satellite by the gravitational pull of the earth is
A) directed toward Earth.
B) directed parallel to Earth's axis and toward the north pole.
C) directed parallel to Earth's axis and toward the south pole.
D) directed toward the satellite.
E) zero.

Free

Multiple Choice

Q 91Q 91

In the figure, the rotational inertia of the wheel and axle about the center is
12)0 kg · m

^{2}, the constant force F is 39.2 N, and the radius r is 0.800 m. The wheel starts from rest. When the force has acted through 2.00 m, the rotational velocity acquired by the wheel due to this force will be A) 1.26 rad/s B) 3.33 rad/s C) 3.61 rad/s D) 6.24 rad/s E) 10.3 rad/sFree

Multiple Choice

Q 92Q 92

Two blocks m

_{1}(= 0.4 kg) and m_{2}(= 0.6 kg) are initially positioned at x = 0.6 and X = 1.1m. One cord is used to couple the blocks together and another to attach m_{1}to a vertical pole at the origin. The blocks are made to rotate in a horizontal circle on a frictionless surface. If the period of rotation is 0.4s then calculate the ratio of the tension for the inner cord divided by the tension in the outer cord. A) 0.64 B) 1.4 C) 1.6 D) 0.74 E) 1.8Free

Multiple Choice

Q 93Q 93

A solid cylinder of mass m = 3 kg and radius r = 12 cm is initially rotating about its central axis with angular frequency = 25 radians/s. How many revolutions does it make after a retarding force of 0.5 N is applied to the outer surface?
A) 0.018 rev
B) 0.11 rev
C) 0.036 rev
D) 0.0090 rev
E) 0.072 rev

Free

Multiple Choice

Q 94Q 94

Use the figure on the right to answer the next problems.
A mass m = 0.5 kg is hung from a pulley with moment of inertia I = 0.20kgm

^{2}and radius R = 10cm. There is friction in the pulley. The mass is dropped from rest, and after 2s it traveled 4m. -What is the angular acceleration of the pulley? A) 2 rad/s^{2}B) 5 rad/s^{2}C) 10 rad/s^{2}D) 20 rad/s^{2}E) 40 rad/s^{2}Free

Multiple Choice

Q 95Q 95

Use the figure on the right to answer the next problems.
A mass m = 0.5 kg is hung from a pulley with moment of inertia I = 0.20kgm

^{2}and radius R = 10cm. There is friction in the pulley. The mass is dropped from rest, and after 2s it traveled 4m. -What is the torque due to friction? A) 0.5 Nm B) 0.9 Nm C) 2.9 Nm D) 3.9 Nm E) 4.5 NmFree

Multiple Choice

Q 96Q 96

A yoyo with moment of inertia I and mass m is hung using a light string over a frictionless pulley. A force F is applied to the other end of the string. The yoyo is allowed to unwind. As the yoyo unwinds, the force needed to stop the pulley from rotating is _____ the weight mg.
A) less than
B) equal to
C) greater than
D) depends how fast the yoyo is unwinding
E) unable to tell

Free

Multiple Choice

Q 97Q 97

Two solid balls (one large, the other small) and a cylinder roll down a hill. Which has the greatest speed at the bottom and which the least?
A) The large ball has the greatest; the small ball has the least.
B) The small ball has the greatest; the large ball has the least.
C) The cylinder has the greatest; the small ball has the least.
D) The cylinder has the greatest; both balls have the same lesser speed.
E) Both balls have the same greater speed; the cylinder has the least.

Free

Multiple Choice

Q 98Q 98

Assume that all of the mass of a bicycle wheel is concentrated at its rim. Such a wheel of mass 1.2 kg and radius 30 cm starts from rest at the top of a hill 100 m long and inclined at 20º to the horizontal. What will be the speed of the wheel at the bottom of the hill if it rolls without slipping?
A) 21 m/s
B) 26 m/s
C) 15 m/s
D) 33 m/s
E) 37 m/s

Free

Multiple Choice

Q 99Q 99

Starting from rest at the same time, a coin and a ring roll down an incline without slipping. Which reaches the bottom first?
A) The ring reaches the bottom first.
B) The coin reaches the bottom first.
C) They arrive at the bottom simultaneously.
D) The winner depends on the relative masses of the two.
E) The winner depends on the relative diameters of the two.

Free

Multiple Choice

Q 100Q 100

For a hoop (ring) of mass M and radius R that is rolling without slipping, which is greater, its translational or its rotational kinetic energy?
A) Its translational kinetic energy is greater.
B) Its rotational kinetic energy is greater.
C) They are equal.
D) The answer depends on the radius.
E) The answer depends on the mass.

Free

Multiple Choice

Q 101Q 101

For a disc of mass M and radius R that is rolling without slipping, which is greater, its translational or its rotational kinetic energy?
A) Its translational kinetic energy is greater.
B) Its rotational kinetic energy is greater.
C) They are equal.
D) The answer depends on the radius.
E) The answer depends on the mass.

Free

Multiple Choice

Q 102Q 102

A wheel on a car is rolling without slipping along level ground. The speed of the car is 36 m/s. The wheel has an outer diameter of 50 cm. The speed of the top of the wheel is
A) 36 m/s
B) 3.6 m/s
C) 72 m/s
D) 18 m/s
E) 98 m/s

Free

Multiple Choice

Q 103Q 103

A bicycle is moving at a speed v = 12.6 m/s. A small stone is stuck to one of the tires. At the instant the stone is at point A in the figure, it comes free. The velocity of the stone (magnitude and direction) relative to Earth just after release is
A) 17.8 m/s at 45º above the horizontal, towards the front of the bicycle.
B) 12.6 m/s at 45º above the horizontal, away from the bicycle.
C) 12.6 m/s at 37º below the horizontal.
D) 12.6 m/s straight up.
E) 17.8 m/s at 45º above the horizontal, towards the back of the bicycle.

Free

Multiple Choice

Q 104Q 104

A wheel of radius R is rolling without slipping. The velocity of the point on the rim that is in contact with the surface, relative to the surface, is
A) equal to R in the direction of motion of the center of mass.
B) equal to R opposite the direction of motion of the center of mass.
C) zero.
D) equal to the velocity of the center of mass and in the same direction.
E) equal to the velocity of the center of mass but in the opposite direction.

Free

Multiple Choice

Q 105Q 105

A solid cylinder, a hollow cylinder, and a square block of equal masses are released at the top of an inclined plane. The cylinders roll down and the block slides down, all with negligible frictional losses. Which of the following will happen?
A) The hollow cylinder arrives at the bottom first.
B) The solid cylinder arrives at the bottom first.
C) The block arrives at the bottom first.
D) They all arrive at the bottom simultaneously.
E) None of these will happen.

Free

Multiple Choice

Q 106Q 106

A solid cylinder, a hollow cylinder, and a square block of equal masses are released at the top of an inclined plane. The cylinders roll down and the block slides down, all with negligible frictional losses. In what order will they arrive at the bottom?
A) solid cylinder, hollow cylinder, block
B) hollow cylinder, solid cylinder, block
C) block, hollow cylinder, solid cylinder
D) block, solid cylinder, hollow cylinder
E) all at the same instant

Free

Multiple Choice

Q 107Q 107

Three solid, homogeneous spheres are on identical inclined planes. If there are no frictional losses, which of the following statements correctly relates the translational speeds at the bottoms of the inclined planes?
A) v

_{A}= v_{B}= v_{C }B) v_{A}> v_{B}; v_{A}> v_{C }C) v_{A}< v_{C}; v_{B}< v_{C }D) v_{A}< v_{B}; v_{B}< v_{C }E) v_{A}= v_{B}; v_{B}< v_{C }Free

Multiple Choice

Q 108Q 108

You are given two hoops (I = mR

^{2}), which are (1) brass and (2) wood, and two cylinders (I = mR^{2}), which are (3) brass and (4) wood; each has radius R. If all are released from the same starting line at the same time, the one(s) that reach the bottom first are A) 1 and 2 B) 3 and 4 C) 1, 2, 3, and 4 D) 1 E) 3Free

Multiple Choice

Q 109Q 109

The moment of inertia of a certain wheel about its axle is mR

^{2}. The translational speed of its axle after it starts from rest and rolls without slipping down an inclined plane 2.13 m high is A) 9.75 m/s B) 8.53 m/s C) 7.31 m/s D) 6.10 m/s E) 4.88 m/sFree

Multiple Choice

Q 110Q 110

A uniform cylinder (I = mR

^{2}) of diameter 0.20 m and mass 12 kg rolls without slipping down a 37º inclined plane. The acceleration of the cylinder down the plane is approximately A) 2.0 m/s^{2 }B) 3.9 m/s^{2 }C) 4.9 m/s^{2 }D) 5.8 m/s^{2 }E) 9.8 m/s^{2 }Free

Multiple Choice

Q 111Q 111

A uniform cylinder (I = mR

^{2}) of diameter 0.20 m and mass 12 kg rolls without slipping down a 37º inclined plane. The gain in translational kinetic energy of the cylinder when it has rolled 5 m down the incline of the plane is approximately A) 24 J B) 0.12 kJ C) 0.24 kJ D) 0.35 kJ E) 0.59 kJFree

Multiple Choice

Q 112Q 112

A solid disk (I

_{cm}= mR^{2}) rolls without slipping up a plane a distance s. The plane is inclined at an angle with the horizontal. The disk has mass m, radius R, and an initial translational speed v. The distance s the disk rolls is A) v^{2}/(g sin ) B) v^{2}/(g sin ) C) Rv/(g sin ) D) mg(sin - cos )(Rv)^{2 }E) v^{2}/(g sin )Free

Multiple Choice

Q 113Q 113

In the laboratory, a solid cylinder is permitted to roll down a plane inclined at an angle with the horizontal. If no slipping occurs, which of the following is true?
A) No slipping implies no frictional force to consider.
B) Because there is no slipping, the motion of the cylinder can be considered to be a pure rotation about the center of mass.
C) The change in potential energy is equal to I

_{0}^{2}. D) The acceleration of the center of mass can be expressed in terms of the acceleration due to gravity and . E) The only force acting on the cylinder is that of gravity.Free

Multiple Choice

Q 114Q 114

The curve that most nearly represents the acceleration of an object rolling down an inclined plane as a function of the angle of inclination is
A) 1
B) 2
C) 3
D) 4
E) 5

Free

Multiple Choice

Q 115Q 115

A 1.0-kg metal hoop with a radius of 0.5 m has a translational velocity of 2.0 m/s as it rolls without slipping. The angular momentum of this hoop about its center of mass is
A) 1.0 kg · m

^{2}/s B) 2.0 kg · m^{2}/s C) 8.0 kg · m^{2}/s D) 4.0 kg · m^{2}/s E) 0.50 kg · m^{2}/sFree

Multiple Choice

Q 116Q 116

A hoop of radius 3.05 n has a mass of 145 kg. Its moment of inertia is mR

^{2}. The hoop rolls without slipping along a horizontal plane. If the center of mass of the hoop has a speed of 0.305 m/s, the work required to bring the hoop to rest is A) 6.78 J B) 13.5 J C) 682 J D) 217 J E) 4.34 kJFree

Multiple Choice

Q 117Q 117

Two uniform discs, each with the same mass but with radii differing by a factor of two, roll without slipping down an inclined plane. If the two discs start from rest at the same height h, calculate the ratio of the angular velocity of the small disc divided by that of the larger disc.
A) 1
B) 0.5
C) 4
D) 2
E) 0.25

Free

Multiple Choice

Q 118Q 118

A solid spherical ball of mass M and radius R rolls without slipping down an inclined plane from a height h. Compare the center of mass speed of the ball at the bottom of the plane with the speed obtained if the ball were simply dropped from a height h.
A) rolling ball is (5/7)

^{1/2}times slower B) rolling ball is 7/5 times faster C) rolling ball is (2/3)^{1/2 }times slower D) rolling ball is 2/3 times faster E) rolling ball and dropped ball have the same speedsFree

Multiple Choice

Q 119Q 119

A spherically symmetric object with mass m = 0.2 kg and radius r = 10 cm, rolls without slipping on a horizontal surface with speed 1 m/s. It then rolls up an incline that is at an angle 30 with the horizon and comes to rest at a distance of 0.6 m along the incline. What is the moment of inertia of the object about an axis through the center of mass?
A) 1.0 10

^{-4}kg · m^{2}/s B) 2.0 10^{-3}kg · m^{2}/s C) 9.8 10^{-3}kg · m^{2}/s D) 1.2 10^{-2}kg · m^{2}/s E) 8.0 10^{-4}kg · m^{2}/sFree

Multiple Choice