# Quiz 7: Rotational Motion

Physics & Astronomy

Q 1Q 1

There must be equal amounts of mass on both sides of the center of mass (or center of gravity)of a system.

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True False

False

Q 2Q 2

When a rigid object rotates about a fixed axis, what is true about all the points in the object? (There could be more than one correct choice.)
A)They all have the same angular speed.
B)They all have the same tangential speed.
C)They all have the same angular acceleration.
D)They all have the same tangential acceleration.
E)They all have the same radial acceleration.

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Multiple Choice

A, C

Q 3Q 3

Two children, Ahmed and Jacques, ride on a merry-go-round. Ahmed is at a greater distance from the axis of rotation than Jacques. Which of the following are true statements? (There could be more than one correct choice.)
A)Jacques has a greater angular speed than Ahmed.
B)Jacques and Ahmed have the same angular speed.
C)Jacques has a smaller angular speed than Ahmed.
D)Ahmed has a greater tangential speed than Jacques.
E)Jacques and Ahmed have the same tangential speed.

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Multiple Choice

B, D

Q 4Q 4

A car is traveling along a freeway at 65 mph. What is the linear speed, relative to the highway, of each of the following points on one of its tires?
(a)the highest point on the tire
(b)the lowest point on a tire
(c)the center of the tire

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Essay

Q 5Q 5

The figure shows scale drawings of four objects, each of the same mass and uniform thickness, with the mass distributed uniformly. Which one has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing at point P?
A)A
B)B
C)C
D)D
E)The moment of inertia is the same for all of these objects.

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Multiple Choice

Q 6Q 6

Two forces produce equal torques on a door about the door hinge. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force has a greater magnitude?
A)the first force (at the midpoint)
B)the second force (at the doorknob)
C)The two forces are equal.

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Multiple Choice

Q 7Q 7

Two equal-magnitude forces are applied to a door at the doorknob. The first force is applied perpendicular to the door, and the second force is applied at 30° to the plane of the door. Which force exerts the greater torque about the door hinge?
A)the first force (applied perpendicular to the door)
B)the second force (applied at an angle)
C)Both forces exert equal non-zero torques.
D)Both forces exert zero torque.

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Multiple Choice

Q 8Q 8

As shown in the figure, a given force is applied to a rod in several different ways. In which case is the torque about the pivot P due to this force the greatest?
A)1
B)2
C)3
D)4
E)5

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Multiple Choice

Q 9Q 9

Five forces act on a rod that is free to pivot at point P, as shown in the figure. Which of these forces is producing a counter-clockwise torque about point P? (There could be more than one correct choice.)
A)force A
B)force B
C)force C
D)force D
E)force E

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Multiple Choice

Q 10Q 10

The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left), or a distance r/2 from the axis of rotation (right). If you release the hanging blocks simultaneously from rest,
A)the block at the left lands first.
B)the block at the right lands first.
C)both blocks land at the same time.

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Multiple Choice

Q 11Q 11

In the figure, four point masses are placed as shown. Assume that all the numbers in the figure are accurate to two significant figures. What are the x and y coordinates of the center of mass (or center of gravity)of this arrangement?
A)(2.2 m, 2.6 m)
B)(2.2 m, 2.7 m)
C)(2.3 m, 2.6 m)
D)(2.3 m, 2.7 m)
E)(2.3 m, 2.8 m)

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Multiple Choice

Q 12Q 12

As shown in the figure, a 60-cm length of uniform wire, of mass 60 g, is bent into a right triangle. What are the x and y coordinates of the center of mass (or center of gravity)of this triangle?
A)(8.0 cm, 3.0 cm)
B)(8.0 cm, 5.0 cm)
C)(9.0 cm, 4.0 cm)
D)(10 cm, 3.0 cm)
E)(10 cm, 5.0 cm)

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Multiple Choice

Q 13Q 13

A 60.0-kg man stands at one end of a 20.0-kg uniform 10.0-m long board. How far from the man is the center of mass (or center of gravity)of the man-board system?
A)1.25 m
B)2.50 m
C)5.00 m
D)7.50 m
E)9.00 m

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Multiple Choice

Q 14Q 14

A 2.0-m rope is lying on a table. You pick up one end and start raising it vertically. How high above the table is the center of mass (or center of gravity)of the rope when half of the rope has lifted off the table?
A)0.25 m
B)0.50 m
C)0.75 m
D)1.0 m
E)1.5 m

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Multiple Choice

Q 15Q 15

Three masses are located in the x-y plane as follows: a mass of 6 kg is at (0 m, 0 m), a mass of 4 kg is at (3 m, 0 m), and a mass of 2 kg is at (0 m, 3 m). Where is the center of mass (or center of gravity)of the system?
A)(1 m, 2 m)
B)(2 m, 1 m)
C)(1 m, 1 m)
D)(1 m, 0.5 m)
E)(0.5 m, 1 m)

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Multiple Choice

Q 16Q 16

Three balls are moving along a straight line having the instantaneous positions shown in the figure. At that instant, find the location and velocity of the center of mass (or center of gravity)of this system.

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Essay

Q 17Q 17

A 30-kg child stands at one end of a floating 20-kg canoe that is 5.0-m long and initially at rest in the water. The child then slowly walks to the other end of the canoe. How far does the canoe move in the water, assuming water friction is negligible?
A)1.0 m
B)2.0 m
C)3.0 m
D)4.0 m
E)5.0 m

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Multiple Choice

Q 18Q 18

The center of mass (or center of gravity)of a two-particle system is at the origin. One particle is located at (3.0 m, 0.0 m)and has a mass of 2.0 kg. The other particle has a mass of 3.0 kg. What is the location of the 3.0-kg particle?
A)(-3.0 m, 0.0 m)
B)(-2.0 m, 0.0 m)
C)(2.0 m, 0.0 m)
D)(3.0 m, 0.0 m)

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Multiple Choice

Q 19Q 19

Three small masses are positioned at the following coordinates: 3.0 kg at (3.0 m, 2.0 m); 4.0 kg at (0.0 m, -1.0 m); and 5.0 kg at (5.0 m, -7.0 m). What are the coordinates of the center of mass (or center of gravity)of this system?

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Essay

Q 20Q 20

Three small masses are positioned as follows: 2.0 kg at (0.0 m, 0.0 m), 2.0 kg at (2.0 m, 0.0 m), and 4.0 kg at (2.0 m, 1.0 m). Determine the coordinates of the center of mass (or center of gravity)of this system.
A)(0.50 m, 1.5 m)
B)(1.5 m, 0.50 m)
C)(2.5 m, 1.5 m)
D)(2.5 m, 0.50 m)

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Multiple Choice

Q 21Q 21

Three masses, 1.0 kg, 2.0 kg, and 3.0 kg, are located at (0.0 m, 0.0 m), (1.0 m, 1.0 m), and (2.0 m, -2.0 m), respectively. What is the location of the center of mass (or center of gravity)of this system?
A)(1.3 m, 0.67 m)
B)(1.3 m, -0.67 m)
C)(-1.3 m, 0.67 m)
D)(-1.3 m, -0.67 m)

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Multiple Choice

Q 22Q 22

A 3.0-kg mass is located at (0.0 m, 8.0 m), and a 1.0-kg mass is located at (12 m, 0.0 m). You want to add a 4.0-kg mass so that the center of mass (or center of gravity)of the three-mass system will be at the origin. What should be the coordinates of the 4.0-kg mass?
A)(-3.0 m, -6.0 m)
B)(-12 m, -8.0 m)
C)(3.0 m, 6.0 m)
D)(-6.0 m, -3.0 m)

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Multiple Choice

Q 23Q 23

A 1.0-g bead is at (-2.0 cm, 2.0 cm), a 2.0-g bead is at (2.0 cm, -4.0 cm), and a 3.0-g bead is at (2.0 cm, 0.0 cm). What are the coordinates of the center of mass (or center of gravity)of this system of beads?

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Essay

Q 24Q 24

Consider the sun and its largest planet Jupiter. On the line joining them, how far from the center of the sun is their center mass? Is it within or outside the sun? (Jupiter-sun distance is 778 × 10

^{6}km, diameter of the sun is 1.4 × 10^{6}km, the sun is 1000 times as massive as Jupiter)Free

Essay

Q 25Q 25

The diameter of the Moon is 3.47 × 10

^{6}m, and it subtends an angle of 0.00904 rad when viewed from the surface of Earth. How far is the Moon from Earth?Free

Essay

Q 26Q 26

The sun subtends an angle of 0.00928 rad when viewed from the surface of the earth, and its distance from Earth is 1.5 × 10

^{11 }m. What is the diameter of the sun?Free

Essay

Q 27Q 27

What is the angular speed, in rad/s, of a flywheel turning at 813.0 rpm?
A)85.14 rad/s
B)13.53 rad/s
C)63.84 rad/s
D)95.33 rad/s

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Multiple Choice

Free

Multiple Choice

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Essay

Q 30Q 30

An artificial satellite in a low orbit circles the earth every 98 minutes. What is its angular speed in rad/s?

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Essay

Q 31Q 31

A chicken is running in a circular path with an angular speed of 1.52 rad/s. How long does it take the chicken to complete one revolution?
A)4.13 s
B)2.07 s
C)118 s
D)4.77 s
E)8.26 s

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Multiple Choice

Q 32Q 32

At a certain instant, a compact disc is rotating at 210 rpm. What is its angular speed in rad/s?
A)11 rad/s
B)22 rad/s
C)45 rad/s
D)69 rad/s
E)660 rad/s

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Multiple Choice

Q 33Q 33

When a fan is turned off, its angular speed decreases from 10 rad/s to 6.3 rad/s in 5.0 s. What is the magnitude of the average angular acceleration of the fan?
A)0.86 rad/s

^{2}B)0.74 rad/s^{2}C)0.37 rad/s^{2}D)11 rad/s^{2}E)1.2 rad/s^{2}Free

Multiple Choice

Q 34Q 34

A bicycle wheel has an outside diameter of 66 cm. Through what distance does a point on the rim move as the wheel rotates through an angle of 70°?

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Essay

Q 35Q 35

When Mary is 3.00 m from the center of a merry-go-round, her tangential speed is a constant 1.88 m/s.
(a)What is her angular speed in rad/s?
(b)What is the magnitude of her linear acceleration?

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Essay

Q 36Q 36

A cylinder of radius 8.0 cm rolls 20 cm in 5.0 s without slipping. Through how many degrees does the cylinder turn during this time?

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Essay

Q 37Q 37

A wheel of diameter 0.70 m rolls on the floor without slipping. A point at the top of the wheel moves with a speed 2.0 m/s relative to the floor.
(a)At what speed is the central axis of the wheel moving relative to the floor?
(b)What is the angular speed of the wheel?

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Essay

Q 38Q 38

A child is riding a merry-go-round that is turning at 7.18 rpm. If the child is standing 4.65 m from the center of the merry-go-round, how fast is the child moving?
A)5.64 m/s
B)3.50 m/s
C)0.556 m/s
D)1.75 m/s
E)1.80 m/s

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Multiple Choice

Q 39Q 39

An electrical motor spins at a constant If the rotor radius is what is the linear acceleration of the edge of the rotor?
A)5707 m/s

^{2}B)281.6 m/s^{2}C)572,400 m/s^{2}D)28.20 m/s^{2}Free

Multiple Choice

Q 40Q 40

A string is wound tightly around a fixed pulley having a radius of 5.0 cm. As the string is pulled, the pulley rotates without any slipping of the string. What is the angular speed of the pulley when the string is moving at 5.0 m/s?
A)100 rad/s
B)50 rad/s
C)25 rad/s
D)20 rad/s
E)10 rad/s

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Multiple Choice

Q 41Q 41

A scooter has wheels with a diameter of 120 mm. What is the angular speed of the wheels when the scooter is moving forward at 6.00 m/s?
A)47.7 rpm
B)955 rpm
C)72.0 rpm
D)50.0 rpm
E)100 rpm

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Multiple Choice

Q 42Q 42

A bicycle has wheels that are 60 cm in diameter. What is the angular speed of these wheels when it is moving at 4.0 m/s?
A)1.2 rad/s
B)4.8 rad/s
C)0.36 rad/s
D)13 rad/s
E)7.6 rad/s

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Multiple Choice

Q 43Q 43

A bowling ball of mass 7.5 kg and diameter 18 cm rolls without slipping down a 10-m bowling lane with a constant speed 4.3 m/s.
(a)Through what angle does the bowling ball turn as it travels the length of the lane?
(b)What is the angular speed of the bowling ball?
(c)Calculate the maximum radial acceleration that a point on the surface of the bowling ball could have.
(d)Calculate the tangential acceleration of a point on the surface of the bowling ball.

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Essay

Q 44Q 44

A rolling wheel of diameter of 68 cm slows down uniformly from 8.4 m/s to rest over a distance of 115 m. What is the magnitude of its angular acceleration if there was no slipping?
A)1.8 rad/s

^{2}B)0.90 rad/s^{2}C)5.7 rad/s^{2}D)11 rad/s^{2}Free

Multiple Choice

Q 45Q 45

A child is riding a merry-go-round that has an instantaneous angular speed of 1.25 rad/s and an angular acceleration of 0.745 rad/s

^{2}. The child is standing 4.65 m from the center of the merry-go-round. What is the magnitude of the linear acceleration of the child? A)8.05 m/s^{2}B)7.27 m/s^{2}C)2.58 m/s^{2}D)3.46 m/s^{2}E)4.10 m/s^{2}Free

Multiple Choice

Q 46Q 46

When an old LP turntable was revolving at 33 rpm, it was shut off and uniformly slowed down and stopped in 5.5 seconds.
(a)What was the magnitude of its angular acceleration (in rad/s

^{2})as it slowed down? (b)Through how many revolutions did it turn while stopping?Free

Essay

Q 47Q 47

A wheel accelerates with a constant angular acceleration of 4.5 rad/s

^{2}from an initial angular speed of 1.0 rad/s. (a)Through what angle does the wheel turn in the first 2.0 s, and (b)what is its angular speed at that time?Free

Essay

Q 48Q 48

A wheel starts from rest and has a uniform angular acceleration of 4.0 rad/s

^{2}. After the wheel completes its first revolution, how long does it take for it to make its second complete revolution?Free

Essay

Q 49Q 49

A bicycle wheel has an initial angular speed of 7.2 rad/s. After turning through of a revolution, the angular speed is reduced to 2.2 rad/s. If the angular acceleration of the wheel was constant during the motion, how long will it take the wheel to make the revolution?

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Essay

Q 50Q 50

How long does it take for a rotating object to speed up from 15.0 rad/s to 33.3 rad/s if it has a uniform angular acceleration of 3.45 rad/s

^{2}? A)4.35 s B)5.30 s C)9.57 s D)10.6 s E)63.1 sFree

Multiple Choice

Q 51Q 51

A wheel accelerates from rest to at a uniform rate of Through what angle (in radians)did the wheel turn while accelerating?
A)30 rad
B)24 rad
C)60 rad
D)38 rad

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Multiple Choice

Q 52Q 52

A machinist turns on the power to a grinding wheel at time t = 0 s. The wheel accelerates uniformly from rest for 10 s and reaches the operating angular speed of The wheel is run at that angular speed for 30 s and then power is shut off. The wheel slows down uniformly at until the wheel stops. In this situation, what is the angular acceleration of the wheel between and
A)3.8 rad/
B)4.6 rad/
C)5.3 rad/
D)6.1 rad/
E)6.8 rad/

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Multiple Choice

Q 53Q 53

A machinist turns on the power on to a grinding wheel at time t = 0 s. The wheel accelerates uniformly from rest for 10 s and reaches the operating angular speed of The wheel is run at that angular velocity for 30 s, and then power is shut off. The wheel slows down uniformly at until the wheel stops. What is the total number of revolutions made by the wheel in this situation?
A)510
B)280
C)320
D)470
E)750

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Multiple Choice

Q 54Q 54

A machinist turns on the power on to a grinding wheel at time t = 0 s. The wheel accelerates uniformly from rest for 10 s and reaches the operating angular speed of The wheel is run at that angular velocity for 40 s and then power is shut off. The wheel slows down uniformly at until the wheel stops. For how long a time after the power is shut off does it take the wheel to stop?
A)64 s
B)62 s
C)66 s
D)68 s
E)70 s

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Multiple Choice

Q 55Q 55

In the figure, point P is on the rim of a wheel of radius 2.0 m. At time t = 0, the wheel is at rest, and P is on the x-axis. The wheel undergoes a uniform counterclockwise angular acceleration of 0.010 rad/s

^{2}about the center O. (a)At time t = 0, what is the tangential acceleration of P? (b)What is the linear speed of P when it reaches the y-axis? (c)What is the magnitude of the net linear acceleration of P when it reaches the y-axis? (d)How long after starting does it take for P to return to its original position on the x-axis?Free

Essay

Q 56Q 56

An old LP record that is originally rotating at 33.3 rad/s is given a uniform angular acceleration of 2.15 rad/s

^{2}. Through what angle has the record turned when its angular speed reaches 72.0 rad/s? A)83.2 rad B)316 rad C)697 rad D)66.8 rad E)948 radFree

Multiple Choice

Q 57Q 57

A wheel rotates through an angle of 13.8 rad as it slows down uniformly from 22.0 rad/s to 13.5 rad/s. What is the magnitude of the angular acceleration of the wheel?
A)0.616 rad/s

^{2}B)5.45 rad/s^{2}C)111 rad/s^{2}D)22.5 rad/s^{2}E)10.9 rad/s^{2}Free

Multiple Choice

Q 58Q 58

A pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41 rad/s

^{2}. Through what angle does the pulley turn in 5.26 s? A)113 rad B)22.6 rad C)42.6 rad D)19.3 rad E)160 radFree

Multiple Choice

Q 59Q 59

An old 78 rpm record rotates through an angle of 320° as it slows down uniformly from 78.0 rpm to 22.8 rpm. What is the magnitude of the angular acceleration of the record?
A)2.34 rad/s

^{2}B)5.46 rad/s^{2}C)6.50 rad/s^{2}D)8.35 rad/s^{2}E)10.9 rad/s^{2}Free

Multiple Choice

Q 60Q 60

A turntable 45 cm in diameter starts from rest and makes its first complete revolution in 3.4 s with constant angular acceleration. If it maintains the same acceleration, how long will it take the turntable to make its second complete revolution?

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Essay

Q 61Q 61

A Ferris wheel rotating at 20 rad/s slows down with a constant angular acceleration of magnitude 5.0 rad/s

^{2}. How many revolutions does it make while slowing down before coming to rest? A)40 B)20 C)6.4 D)3.2Free

Multiple Choice

Q 62Q 62

A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it makes 50 complete turns at a constant angular acceleration before coming to rest.
(a)What was the magnitude of the angular acceleration of the centrifuge as it slowed down?
(d)How long did it take for the centrifuge to come to rest after being turned off?

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Essay

Q 63Q 63

A majorette fastens two batons together at their centers to form an X shape. Each baton consists of an extremely light 1.2-m bar with small 0.25-kg balls at each end. What is the moment of inertia of this baton about an axis through the center of the X?

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Essay

Q 64Q 64

A triatomic molecule is oriented as follows along the x-axis: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia of this molecule about the y-axis?
A)2ma

^{2}B)3ma^{2}C)12ma^{2}D)14ma^{2}Free

Multiple Choice

Q 65Q 65

Two uniform solid spheres have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia about a central axis to that of the smaller sphere is
A)4/5.
B)8/5.
C)1/2.
D)2.
E)4.

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Multiple Choice

Q 66Q 66

The L-shaped object shown in the figure consists of three small masses connected by extremely light rods. Assume that the masses shown are accurate to three significant figures. What is the moment of inertia of this object (a)about the x-axis, and (b)about the y-axis?

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Essay

Q 67Q 67

The L-shaped object shown in the figure consists of three small masses connected by thin uniform rods, each rod of mass 3.00 kg. Assume that the masses shown are accurate to three significant figures. What is the moment of inertia of this object (a)about the x-axis, and (b)about the y-axis?

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Essay

Q 68Q 68

In the figure, a weightlifter's barbell consists of two identical small but dense spherical weights, each of mass 50 kg. These weights are connected by a thin 0.96-m rod with a mass of 24 kg. Find the moment of inertia of the barbell through the axis perpendicular to the rod at its center, assuming the two weights are small enough to be treated as point masses.

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Essay

Q 69Q 69

A potter's wheel has the shape of a solid uniform disk of mass and radius 0.65 m. It spins about an axis perpendicular to the disk at its center. A small 2.1 kg lump of very dense clay is dropped onto the wheel at a distance 0.41 m from the axis. What is the moment of inertia of the system about the axis of spin?
A)1.8 kg ∙ m

^{2}B)1.5 kg ∙ m^{2}C)0.40 kg ∙ m^{2}D)2.5 kg ∙ m^{2}Free

Multiple Choice

Q 70Q 70

The lug nuts on a car wheel require tightening to a torque of 90 N ∙ m. If a 30-cm long wrench is used, what is the magnitude of the minimum force required using the wrench?
A)300 N
B)150 N
C)30 N
D)15 N

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Multiple Choice

Q 71Q 71

A man in a gym is holding an 8.0-kg weight at arm's length, a distance of 0.55 m from his shoulder joint. What is the torque about his shoulder joint due to the weight if his arm is horizontal?
A)0.24 N ∙ m
B)4.4 N ∙ m
C)43 N ∙ m
D)15 N ∙ m
E)0 N ∙ m

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Multiple Choice

Q 72Q 72

A man in a gym is holding an 8.0-kg weight at arm's length, a distance of 0.55 m from his shoulder joint. What is the torque about his shoulder joint due to the weight if his arm is held at 30° below the horizontal?
A)22 N ∙ m
B)2.2 N ∙ m
C)4.4 N ∙ m
D)13 N ∙ m
E)37 N ∙ m

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Multiple Choice

Q 73Q 73

A force of 17 N is applied to the end of a 0.63-m long torque wrench at an angle 45° from a line joining the pivot point to the handle. What is the magnitude of the torque about the pivot point produced by this force?
A)7.6 N ∙ m
B)10.7 N ∙ m
C)12.0 N ∙ m
D)9.7 N ∙ m

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Multiple Choice

Q 74Q 74

A 95-N force exerted at the end of a 0.32-m long torque wrench produces a torque of 15 N ∙ m. What is the angle (less than 90°)between the wrench handle and the direction of the applied force?
A)30°
B)24°
C)36°
D)42°

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Multiple Choice

Q 75Q 75

The figure shows a person's foot. In that figure, the Achilles tendon exerts a force of magnitude F = 720 N. What is the magnitude of the torque that this force produces about the ankle joint?
A)12 N ∙ m
B)16 N ∙ m
C)21 N ∙ m
D)26 N ∙ m
E)36 N ∙ m

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Multiple Choice

Q 76Q 76

The drive chain in a bicycle is applying a torque of 0.850 N ∙ m to the wheel of the bicycle. The wheel has a moment of inertia of 0.100 kg ∙ m

^{2}. What is the angular acceleration of the wheel?Free

Essay

Q 77Q 77

The drive chain in a bicycle is applying a torque of 0.850 N ∙ m to the wheel of the bicycle. You can treat the wheel as a thin uniform hoop (or ring)with a mass of 0.750 kg and a radius of 33.0 cm. What is the angular acceleration of the wheel?
A)10.4 rad/s

^{2}B)20.8 rad/s^{2}C)5.20 rad/s^{2}D)3.43 rad/s^{2}E)1.06 rad/s^{2}Free

Multiple Choice

Q 78Q 78

A mechanic is examining the wheel of a bicycle to adjust the brake. With the bicycle off the ground, he manually rotates the wheel until it reaches an angular speed of 12.0 rad/s and then allows it to coast to a stop. If the wheel has a moment of inertia of 0.100 kg ∙ m

^{2}, and the wheel slows uniformly to a stop in 160 s, what is the magnitude of the retarding torque? A)1.00 N ∙ m B)0.00750 N ∙ m C)0.0787 N ∙ m D)1.33 N ∙ m E)1.67 N ∙ mFree

Multiple Choice

Q 79Q 79

A force of is applied tangentially to a wheel of radius 0.340 m and causes an angular acceleration of 1.20 rad/s

^{2}. What is the moment of inertia of the wheel? A)4.78 kg ∙ m^{2}B)3.59 kg ∙ m^{2}C)5.98 kg ∙ m^{2}D)7.17 kg ∙ m^{2}Free

Multiple Choice

Q 80Q 80

A torque of 12 N ∙ m is applied to a solid, uniform disk of radius 0.50 m. If the disk accelerates at what is the mass of the disk?
A)60 kg
B)45 kg
C)30 kg
D)15 kg

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Multiple Choice

Q 81Q 81

A particular motor can provide a maximum torque of 110 N ∙ m. Assuming that all of this torque is used to accelerate a solid, uniform, cylindrical flywheel of mass 10.0 kg and radius 3.00 m, how long will it take for the flywheel to accelerate from rest to
A)3.33 s
B)2.83 s
C)4.03 s
D)4.36 s

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Multiple Choice

Q 82Q 82

The drum shown in the figure has a radius of 0.40 m and a moment of inertia of 2.3 about an axis perpendicular to it through its center. The frictional torque at the drum axle is 3.0 N ∙ m. A 14-m length of rope is wound around the rim. The drum is initially at rest. A constant force is applied to the free end of the rope until the rope is completely unwound and slips off. At that instant, the angular speed of the drum is The drum then slows down at a constant rate and comes to a halt. In this situation, what was the magnitude of the constant force applied to the rope?
A)51 N
B)40 N
C)29 N
D)18 N
E)7.5 N

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Multiple Choice

Q 83Q 83

In a laboratory experiment, a student brings up the rotational speed of a flywheel to 30.0 rpm. She then allows it to slow down on its own, and counts 240 revolutions before the apparatus uniformly comes to a stop. The moment of inertia of the flywheel is 0.0850 kg ∙ m

^{2}. What is the magnitude of the retarding torque on the flywheel? A)0.0425 N ∙ m B)0.159 N ∙ m C)0.0787 N ∙ m D)0.000278 N ∙ m E)0.0000136 N ∙ mFree

Multiple Choice

Q 84Q 84

A uniform, solid, 100-kg cylinder with a diameter of 1.0 m is mounted so it is free to rotate about fixed, horizontal, frictionless axis that passes through the centers of its circular ends. A 10-kg block is hung from a very light thin cord wrapped around the cylinder's circumference. When the block is released, the cord unwinds and the block accelerates downward, as shown in the figure. What is the acceleration of the block?

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Q 85Q 85

A cinder block of mass m = 4.0 kg is hung from a nylon string that is wrapped around a frictionless pulley having the shape of a cylindrical shell, as shown in the figure. If the cinder block accelerates downward at 4.90 m/s

^{2}when it is released, what is the mass M of the pulley? A)2.0 kg B)4.0 kg C)6.0 kg D)8.0 kg E)10 kgFree

Multiple Choice

Q 86Q 86

A uniform rod is 2.0 m long. It is hinged to a wall at its left end, and held in a horizontal position at its right end by a vertical very light string, as shown in the figure. What is the angular acceleration of the rod at the moment after the string is released if there is no friction in the hinge?
A)15 rad/s

^{2}B)3.3 rad/s^{2}C)7.4 rad/s^{2}D)11 rad/s^{2}E)It cannot be calculated without knowing the mass of the rod.Free

Multiple Choice

Q 87Q 87

A uniform solid cylinder of mass 10 kg can rotate about a frictionless axle through its center O, as shown in the cross-sectional view in the figure. A rope wrapped around the outer radius R

_{1}= 1.0 m exerts a force of magnitude F_{1}= 5.0 N to the right. A second rope wrapped around another section of radius R_{2}= 0.50 m exerts a force of magnitude F_{2}= 6.0 N downward. What is the angular acceleration of the cylinder? A)1.0 rad/s^{2}B)0.60 rad/s^{2}C)0.40 rad/s^{2}D)0.80 rad/s^{2}Free

Multiple Choice

Q 88Q 88

A uniform solid cylinder of mass 10 kg can rotate about a frictionless axle through its center O, as shown in the cross-sectional view in the figure. A rope wrapped around the outer radius R

_{1}= 1.0 m exerts a force of magnitude F_{1}= 5.0 N to the right. A second rope wrapped around another section of radius R_{2}= 0.50 m exerts a force of magnitude F_{2}= 6.0 N downward. How many radians does the cylinder rotate through in the first 5.0 seconds, if it starts from rest? A)13 rad B)7.5 rad C)5.0 rad D)10 radFree

Multiple Choice

Q 89Q 89

The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left), or a distance r/2 from the axis of rotation (right). If you release the hanging blocks simultaneously from rest, and call t

_{L}the time taken by the block on the left and t_{R}the time taken by the block on the right to reach the bottom, respectively, then A)t_{L}> t_{R}. B)t_{L}= t_{R}. C)t_{L}< t_{R}.Free

Multiple Choice

Q 90Q 90

A 1.53-kg bucket hangs on a rope wrapped around a pulley of mass 7.07 kg and radius 66 cm. This pulley is frictionless in its axle, and has the shape of a solid uniform disk. After the bucket has been released, (a)what is the angular acceleration of the pulley, and (b)what is the acceleration of the bucket?

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Q 91Q 91

A 350-g air track cart on a horizontal air track is attached to a string that goes over a frictionless pulley with a moment of inertia of 6.00 × 10

^{-6}kg ∙ m^{2 }and a radius of 1.35 cm. If the string is pulled vertically downward by a force of 2.50 N, (a)what is the magnitude of the acceleration of the cart, and (b)what is the tension in the horizontal string between the pulley and the cart?Free

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Q 92Q 92

A 375-g stone hangs from a thin light string that is wrapped around the circumference of a frictionless pulley with a moment of inertia of 0.0125 kg ∙ m

^{2}and a radius of 26 cm. When the stone is released, the stone accelerates downward and the pulley rotates about its axis as the string unwinds. (a)What is the magnitude of the acceleration of the stone? (b)What is the tension in the string?Free

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Q 93Q 93

As shown in the figure, a 35.30-kg box is attached to a light string that is wrapped around a cylindrical frictionless spool of radius 10.0 cm and moment of inertia 4.00 kg ∙ m

^{2}. The spool is suspended from the ceiling, and the box is then released from rest a distance 3.50 m above the floor. How long does it take for the box to reach the floor? A)2.97 s B)2.85 s C)0.892 s D)4.18 s E)5.89 sFree

Multiple Choice

Q 94Q 94

A 385-g tile hangs from one end of a string that goes over a pulley with a moment of inertia of and a radius of 15.0 cm. A mass of 710 g hangs from the other end of the string. When the tiles are released, the larger one accelerates downward while the lighter one accelerates upward. The pulley has no friction in its axle and turns without the string slipping. What is the tension in the string on the side of the 710-g tile?
A)9.77 N
B)6.87 N
C)5.59 N
D)4.41 N
E)3.68 N

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Multiple Choice

Q 95Q 95

A small 355-g box hangs from one end of a thin light string that goes over a frictionless pulley having a moment of inertia of 0.0125 kg ∙ m

^{2}and a radius of 15 cm. A second small package, this one of mass 680 g, hangs from the other end of the string. When the packages are released, the larger one accelerates downward, the lighter one accelerates upward, and the pulley turns without the string slipping. (a)What is the tension in the string on the side of the 355-g package? (b)At what rate do the packages change their speeds?Free

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