# Quiz 10: Rotation

Physics & Astronomy

Free

Multiple Choice

D

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Multiple Choice

E

Q 3Q 3

One revolution per minute is about:
A)0.0524 rad/s
B)0.105 rad/s
C)0.95 rad/s
D)1.57 rad/s
E)6.28 rad/s

Free

Multiple Choice

B

Q 4Q 4

If a wheel turns with constant angular speed then:
A)each point on its rim moves with constant velocity
B)each point on its rim moves with constant acceleration
C)the wheel turns through equal angles in equal times
D)the angle through which the wheel turns in each second increases as time goes on
E)the angle through which the wheel turns in each second decreases as time goes on

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Multiple Choice

Q 5Q 5

One-dimensional linear position is measured along a line, from a point designated x = 0.One-dimensional angular position:
A)is measured along a line, from a point designated θ = 0.
B)is measured along the axis of rotation.
C)is the angle that an internal reference line makes with a fixed external reference line.
D)is measured relative to the positive y axis.
E)is meaningless, as rotations take place in two dimensions.

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Multiple Choice

Q 6Q 6

An object rotates from θ

_{1}to θ_{2}through an angle that is less than 2π radians.Which of the following represents its angular displacement? A)θ_{1}B)θ_{2}C)θ_{1}- θ_{2}D)θ_{2}- θ_{1}E)θ_{1}+ θ_{2}Free

Multiple Choice

Q 7Q 7

If a wheel is turning at 3.0 rad/s, the time it takes to complete one revolution is about:
A)0.33 s
B)0.67 s
C)1.0 s
D)1.3 s
E)2.1 s

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Multiple Choice

Q 8Q 8

If a wheel turning at a constant rate completes 100 revolutions in 10 s its angular speed is:
A)0.31 rad/s
B)0.63 rad/s
C)10 rad/s
D)31 rad/s
E)63 rad/s

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Multiple Choice

Q 9Q 9

The angular speed of the second hand of a watch is:
A)(/1800)rad/s
B)(/60)rad/s
C)(/30)rad/s
D)(2)rad/s
E)(60)rad/s

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Multiple Choice

Q 10Q 10

The angular speed of the minute hand of a watch is:
A)(60/)rad/s
B)(1800/)rad/s
C)()rad/s
D)(/1800)rad/s
E)(/60)rad/s

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Multiple Choice

Q 11Q 11

A child, riding on a large merry-go-round, travels a distance of 3000 m in a circle of diameter 40 m.The total angle through which she revolves is:
A)50 rad
B)75 rad
C)150 rad
D)314 rad
E)none of these

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Multiple Choice

Q 12Q 12

Ten seconds after an electric fan is turned on, the fan rotates at 300 rev/min.Its average angular acceleration is:
A)3.14 rad/s

^{2}B)30 rad/s^{2}C)30 rev/s^{2}D)50 rev/min^{2}E)1800 rev/s^{2}Free

Multiple Choice

Q 13Q 13

A flywheel rotating at 12 rev/s is brought to rest in 6 s.The magnitude of the average angular acceleration of the wheel during this process is:
A)1/ rad/s

^{2}B)2 rad/s^{2}C)4 rad/s^{2}D)4 rad/s^{2}E)72 rad/s^{2}Free

Multiple Choice

Q 14Q 14

A phonograph turntable, initially rotating at 0.75 rev/s, slows down and stops in 30 s.The magnitude of its average angular acceleration for this process is:
A)1.5 rad/s

^{2}B)1.5 rad/s^{2}C)/40 rad/s^{2}D)/20 rad/s^{2}E)0.75 rad/s^{2}Free

Multiple Choice

Q 15Q 15

If the angular velocity vector of a spinning body points out of the page then, when viewed from above the page, the body is spinning:
A)clockwise about an axis that is perpendicular to the page
B)counterclockwise about an axis that is perpendicular to the page
C)about an axis that is parallel to the page
D)about an axis that is changing orientation
E)about an axis that is getting longer

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Multiple Choice

Q 16Q 16

The angular velocity vector of a spinning body points out of the page.If the angular acceleration vector points into the page then:
A)the body is slowing down
B)the body is speeding up
C)the body is starting to turn in the opposite direction
D)the axis of rotation is changing orientation
E)none of the above

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Multiple Choice

Q 17Q 17

The angular velocity of a rotating wheel increases 2 rev/s every minute.The angular acceleration of this wheel is:
A)4

^{2}rad/s^{2}B)2 rad/s^{2}C)1/30 rad/s^{2}D)2/30 rad/s^{2}E)4 rad/s^{2}Free

Multiple Choice

Q 18Q 18

A wheel initially has an angular velocity of 18 rad/s.It has a constant angular acceleration of 2.0 rad/s

^{2 }and is slowing at first.What time elapses before its angular velocity is18 rad/s in the direction opposite to its initial angular velocity? A)3.0 s B)6.0 s C)9.0 s D)18 s E)36 sFree

Multiple Choice

Q 19Q 19

A wheel initially has an angular velocity of 36 rad/s but after 6.0s its angular velocity is 24 rad/s.If its angular acceleration is constant the value is:
A)2.0 rad/s

^{2}B)-2.0 rad/s^{2}C)3.0 rad/s^{2}D)-3.0 rad/s^{2}E)6.0 rad/s^{2}Free

Multiple Choice

Q 20Q 20

A wheel initially has an angular velocity of -36 rad/s but after 6.0 s its angular velocity is -24 rad/s.If its angular acceleration is constant the value is:
A)2.0 rad/s

^{2}B)-2.0 rad/s^{2}C)3.0 rad/s^{2}D)-3.0 rad/s^{2}E)-6.0 rad/s^{2}Free

Multiple Choice

Q 21Q 21

An object rotates from θ

_{1}to θ_{2}through an angle that is less than π radians.Which of the following results in a positive angular displacement? A)θ_{1 }= 45°, θ_{2}= −45° B)θ_{1 }= 45°, θ_{2}= 15° C)θ_{1 }= 45°, θ_{2}= −45° D)θ_{1 }= 135°, θ_{2}= −135° E)θ_{1 }= −135°, θ_{2}= 135°Free

Multiple Choice

Q 22Q 22

The coordinate of an object is given as a function of time by θ = 7t - 3t

^{2}, where θ is in radians and t is in seconds.Its average velocity over the interval from t = 0 to t = 2 s is: A)5 rad/s B)-5 rad/s C)11 rad/s D)-11 rad/s E)1 rad/sFree

Multiple Choice

Q 23Q 23

The coordinate of an object is given as a function of time by θ = 7t - 3t

^{2}, where θ is in radians and t is in seconds.Its angular velocity at t = 3 s is: A)−11 rad/s B)−3.7 rad/s C)1.0 rad/s D)3.7 rad/s E)11 rad/sFree

Multiple Choice

Q 24Q 24

This graph shows the angular position of an object as a function of time.What is its average angular velocity between t = 5 s and t = 9 s?
A)3 rad/s
B)−3 rad/s
C)12 rad/s
D)−12 rad/s
E)Need additional information.

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Multiple Choice

Q 25Q 25

This graph shows the angular position of an object as a function of time.What is its instantaneous angular velocity at t = 1.5 s?
A)−6 rad/s
B)6 rad/s
C)9 rad/s
D)12 rad/s
E)Need additional information.

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Multiple Choice

Q 26Q 26

Instantaneous angular speed is:
A)total angular displacement divided by time
B)the integral of the displacement over time
C)the rate at which the angular acceleration is changing
D)the magnitude of the instantaneous angular velocity
E)a vector directed along the axis of rotation

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Multiple Choice

Q 27Q 27

The angular velocity of a rotating turntable is given in rad/s by ω(t)= 4.5 + 0.64t - 2.7t

^{2}.What is its angular acceleration at t = 2.0 s? A)−10 rad/s^{2 }B)-5.0 rad/s^{2}C)−5.4 rad/s^{2}D)2.4 rad/s^{2}E)3.1 rad/s^{2}Free

Multiple Choice

Q 28Q 28

The angular velocity of a rotating turntable is given in rad/s by ω(t)= 4.5 + 0.64t - 2.7t

^{2}.What is its average angular acceleration between t = 1.0 s and t = 3.0 s? A)0.64 rad/s^{2}B)−5.4 rad/s^{2}C)−7.7 rad/s^{2}D)−10 rad/s^{2}E)−27 rad/s^{2}Free

Multiple Choice

Q 29Q 29

This graph shows the angular velocity of a turntable as a function of time.What is its angular acceleration at t = 3.5 s?
A)−10 rad/s

^{2 }B)−5 rad/s^{2}C)0 rad/s^{2}D)5 rad/s^{2}E)10 rad/s^{2}Free

Multiple Choice

Q 30Q 30

This graph shows the angular velocity of a turntable as a function of time.What is its average angular acceleration between t = 2 s and t = 4 s?
A)−10 rad/s

^{2 }B)−5 rad/s^{2}C)0 rad/s^{2}D)5 rad/s^{2}E)10 rad/s^{2}Free

Multiple Choice

Q 31Q 31

A wheel starts from rest and has an angular acceleration that is given by (t)= (6.0 rad/s

^{4})t^{2.}After it has turned through 10 rev its angular velocity is: A)63 rad/s B)75 rad/s C)89 rad/s D)130 rad/s E)210 rad/sFree

Multiple Choice

Q 32Q 32

A wheel is spinning at 27 rad/s but is slowing with an angular acceleration that has a magnitude given by (3.0 rad/s

^{4})t^{2.}It stops in a time of: A)1.7 s B)2.6 s C)3.0 s D)4.4 s E)9.0 sFree

Multiple Choice

Q 33Q 33

A wheel starts from rest and has an angular acceleration that is given by (t)= 6 rad/s

^{4})t^{2.}The angle through which it turns in time t is given by: A)[(1/8)t^{4}] rad/s^{4}B)[(1/4)t^{4}] rad/s^{4}C)[(1/2)t^{4}] rad/s^{4}D)(t^{4})rad/s^{4}E)12 radFree

Multiple Choice

Q 34Q 34

A wheel starts from rest and has an angular acceleration that is given by (t)= (6.0 rad/s

^{4})t^{2}.The time it takes to make 10 rev is: A)1.3 s B)2.1 s C)2.8 s D)3.3 s E)4.0 sFree

Multiple Choice

Q 35Q 35

A flywheel is initially rotating at 20 rad/s and has a constant angular acceleration.After 9.0 s it has rotated through 450 rad.Its angular acceleration is:
A)3.3 rad/s
B)4.4 rad/s
C)6.7 rad/s
D)11 rad/s
E)48 rad/s

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Multiple Choice

Q 36Q 36

A wheel rotates with a constant angular acceleration of rad/s

^{2}.During a certain time interval_{ }its angular displacement is rad.At the end of the interval its angular velocity is 2 rad/s.Its angular velocity at the beginning of the interval is: A)0 rad/s B)1 rad/s C) rad/s D)rad/s E)2 rad/sFree

Multiple Choice

Q 37Q 37

A wheel initially has an angular velocity of 18 rad/s but it is slowing at a rate of 2.0 rad/s

^{2}.By the time it stops it will have turned through: A)81 rad B)160 rad C)245 rad D)330 rad E)410 radFree

Multiple Choice

Q 38Q 38

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

^{2}.When it has made 10 rev its angular velocity is: A)8.9 rad/s B)16 rad/s C)22 rad/s D)32 rad/s E)250 rad/sFree

Multiple Choice

Q 39Q 39

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

^{2}.The time it takes to make 10 revolutions is: A)0.50 s B)0.71 s C)2.2 s D)2.8 s E)5.6 sFree

Multiple Choice

Q 40Q 40

A wheel of diameter 3.0 cm has a 4.0 m cord wrapped around its periphery.Starting from rest, the wheel is given a constant angular acceleration of 2 rad/s

^{2}.The cord will unwind in: A)0.82 s B)2.0 s C)12 s D)16 s E)130 sFree

Multiple Choice

Q 41Q 41

The figure shows a cylinder of radius 0.7 m rotating about its axis at 10 rad/s.The speed of the point P is:
A)7.0 m/s
B)14 rad/s
C)7 rad/s
D)0.70 m/s
E)none of these

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Multiple Choice

Q 42Q 42

A particle moves in a circular path of radius 0.10 m with a constant angular speed of 5 rev/s.The acceleration of the particle is:
A)0.10 m/s

^{2}B)0.50 m/s^{2}C)500 m/s^{2}D)2.5 m/s^{2}E)10^{2}m/s^{2}Free

Multiple Choice

Q 43Q 43

A car travels north at constant velocity.It goes over a piece of mud which sticks to the tire.The initial acceleration of the mud, as it leaves the ground, is:
A)vertically upward
B)horizontally to the north
C)horizontally to the south
D)zero
E)upward and forward at 45 to the horizontal

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Multiple Choice

Q 44Q 44

Wrapping paper is being unwrapped from a 5.0-cm radius tube, free to rotate on its axis.If it is pulled at the constant rate of 10 cm/s and does not slip on the tube, the angular velocity of the tube is:
A)2.0 rad/s
B)5.0 rad/s
C)10 rad/s
D)25 rad/s
E)50 rad/s

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Multiple Choice

Q 45Q 45

String is wrapped around the periphery of a 5.0-cm radius cylinder, free to rotate on its axis.The string is pulled straight out at a constant rate of 10 cm/s and does not slip on the cylinder.As each small segment of string leaves the cylinder, the segment's acceleration changes by:
A)0 m/s

^{2}B)0.010 m/s^{2}C)0.020 m/s^{2}D)0.10 m/s^{2}E)0.20 m/s^{2}Free

Multiple Choice

Q 46Q 46

A flywheel of diameter 1.2 m has a constant angular acceleration of 5.0 rad/s

^{2}.The tangential acceleration of a point on its rim is: A)5.0 rad/s^{2}B)3.0 m/s^{2}C)5.0 m/s^{2}D)6.0 m/s^{2}E)12 m/s^{2}Free

Multiple Choice

Q 47Q 47

For a wheel spinning with constant angular acceleration on an axis through its center, the ratio of the speed of a point on the rim to the speed of a point halfway between the center and the rim is:
A)1
B)2
C)1/2
D)4
E)1/4

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Multiple Choice

Q 48Q 48

For a wheel spinning on an axis through its center, the ratio of the tangential acceleration of a point on the rim to the tangential acceleration of a point halfway between the center and the rim is:
A)1
B)2
C)1/2
D)4
E)1/4

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Multiple Choice

Q 49Q 49

For a wheel spinning on an axis through its center, the ratio of the radial acceleration of a point on the rim to the radial acceleration of a point halfway between the center and the rim is:
A)1
B)2
C)1/2
D)4
E)1/4

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Multiple Choice

Q 50Q 50

Two wheels are identical but wheel B is spinning with twice the angular speed of wheel A.The ratio of the magnitude of the radial acceleration of a point on the rim of B to the magnitude of the radial acceleration of a point on the rim of A is:
A)1
B)2
C)1/2
D)4
E)1/4

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Multiple Choice

Q 51Q 51

The magnitude of the acceleration of a point on a spinning wheel is increased by a factor of 4 if:
A)the magnitudes of the angular velocity and the angular acceleration are each multiplied by a factor of 4
B)the magnitude of the angular velocity is multiplied by a factor of 4 and the angular acceleration is not changed
C)the magnitudes of the angular velocity and the angular acceleration are each multiplied by a factor of 2
D)the magnitude of the angular velocity is multiplied by a factor of 2 and the angular acceleration is not changed
E)the magnitude of the angular velocity is multiplied by a factor of 2 and the magnitude of the angular acceleration is multiplied by a factor of 4

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Multiple Choice

Q 52Q 52

A wheel starts from rest and spins with a constant angular acceleration.As time goes on the acceleration vector for a point on the rim:
A)decreases in magnitude and becomes more nearly tangent to the rim
B)decreases in magnitude and becomes more nearly radial
C)increases in magnitude and becomes more nearly tangent to the rim
D)increases in magnitude and becomes more nearly radial
E)increases in magnitude but retains the same angle with the tangent to the rim

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Multiple Choice

Q 53Q 53

Three identical balls are tied by light strings to the same rod and rotate around it, as shown below.Rank the balls according to their rotational inertia, least to greatest.
A)1, 2, 3
B)3, 2, 1
C)3, then 1 and 2 tie
D)1, 3, 2
E)All are the same

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Multiple Choice

Q 54Q 54

Four identical particles, each with mass m, are arranged in the x, y plane as shown.They are connected by light sticks to form a rigid body.If m = 2.0 kg and a = 1.0 m, the rotational inertia of this array about the y-axis is:
A)4.0 kg∙m

^{2}B)12 kg∙m^{2}C)9.6 kg∙m^{2}D)4.8 kg∙m^{2}E)none of theseFree

Multiple Choice

Q 55Q 55

Three balls, with masses of 3M, 2M, and M, are fastened to a massless rod of length L as shown.The rotational inertia about the left end of the rod is:
A)ML

^{2}/2 B)ML^{2}C)3ML^{2}/2 D)6ML^{2}E)3ML^{2}Free

Multiple Choice

Q 56Q 56

A pulley with a radius of 3.0 cm and a rotational inertia of 4.5 10

^{-3}kg∙m^{2}is suspended from the ceiling.A rope passes over it with a 2.0-kg block attached to one end and a 4.0-kg block attached to the other.The rope does not slip on the pulley.When the velocity of the heavier block is 2.0 m/s the total kinetic energy of the pulley and blocks is: A)2.0 J B)12 J C)14 J D)22 J E)28 JFree

Multiple Choice

Q 57Q 57

A pulley with a radius of 3.0 cm and a rotational inertia of 4.5 10

^{-3}kg∙m^{2}is suspended from the ceiling.A rope passes over it with a 2.0-kg block attached to one end and a 4.0-kg block attached to the other.The rope does not slip on the pulley.At any instant after the blocks start moving the object with the greatest kinetic energy is: A)the heavier block B)the lighter block C)the pulley D)either block (the two blocks have the same kinetic energy) E)none (all three objects have the same kinetic energy)Free

Multiple Choice

Q 58Q 58

The rotational inertia of a thin cylindrical shell of mass M, radius R, and length L about its central axis (X - X')is:
A)MR

^{2}/2 B)ML^{2}/2 C)ML^{2}D)MR^{2}E)none of theseFree

Multiple Choice

Q 59Q 59

The rotational inertia of a wheel about its axle does not depend upon its:
A)diameter
B)mass
C)distribution of mass
D)speed of rotation
E)material composition

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Multiple Choice

Q 60Q 60

A and B are two solid cylinders made of aluminum.Their dimensions are shown.The ratio of the rotational inertia of B to that of A about the common axis X─X' is:
A)2
B)4
C)8
D)16
E)32

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Multiple Choice

Q 61Q 61

Two uniform circular disks having the same mass and the same thickness are made from different materials.The disk with the smaller rotational inertia is:
A)the one made from the more dense material
B)the one made from the less dense material
C)neither - both rotational inertias are the same
D)the disk with the larger angular velocity
E)the disk with the larger torque

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Multiple Choice

Q 62Q 62

A uniform solid cylinder made of lead has the same mass and the same length as a uniform solid cylinder made of wood.The rotational inertia of the lead cylinder compared to the wooden one is:
A)greater
B)less
C)same
D)unknown unless the radii are given
E)unknown unless both the masses and the radii are given

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Multiple Choice

Q 63Q 63

To increase the rotational inertia of a solid disk about its axis without changing its mass:
A)drill holes near the rim and put the material near the axis
B)drill holes near the axis and put the material near the rim
C)drill holes at points on a circle near the rim and put the material at points between the holes
D)drill holes at points on a circle near the axis and put the material at points between the holes
E)do none of the above (the rotational inertia cannot be changed without changing the mass)

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Multiple Choice

Q 64Q 64

The rotational inertia of a disk about its axis is 0.70 kgm

^{2}.When a 2.0 kg weight is added to its rim, 0.40 m from the axis, the rotational inertia becomes: A)0.32 kgm^{2}B)0.54 kgm^{2}C)0.70 kgm^{2}D)0.86 kgm^{2}E)1.0 kgm^{2}Free

Multiple Choice

Q 65Q 65

A thin rod of length L has a density that increases along its length, ρ = ρ

_{0}x.What is the rotational inertia of the rod around its less dense end? A)ML^{2}/12 B)ML^{2}/6 C)ML^{2}/3 D)ML^{2}/2 E)ML^{2}Free

Multiple Choice

Q 66Q 66

When a thin uniform stick of mass M and length L is pivoted about its midpoint, its rotational inertia is ML

^{2}/12.When pivoted about a parallel axis through one end, its rotational inertia is: A)ML^{2}/12 B)ML^{2}/6 C)ML^{2}/3 D)7ML^{2}/12 E)13ML^{2}/12Free

Multiple Choice

Q 67Q 67

The rotational inertia of a solid uniform sphere about a diameter is (2/5)MR

^{2}, where M is its mass and R is its radius.If the sphere is pivoted about an axis that is tangent to its surface, its rotational inertia is: A)MR^{2}B)(2/5)MR^{2}C)(3/5)MR^{2}D)(5/2)MR^{2}E)(7/5)MR^{2}Free

Multiple Choice

Q 68Q 68

A solid uniform sphere of radius R and mass M has a rotational inertia about a diameter that is given by (2/5)MR

^{2}.A light string of length 2.5 R is attached to the surface and used to suspend the sphere from the ceiling.Its rotational inertia about the point of attachment at the ceiling is: A)(2/5)MR^{2}B)9MR^{2}C)16MR^{2}D)47/5MR^{2}E)(82/5)MR^{2}Free

Multiple Choice

Q 69Q 69

The torque exerted on an object can be written as .Here, :
A)is the radius of the object.
B)is a vector pointing from the axis of rotation to the point where the force is applied.
C)is always perpendicular to .
D)is a vector pointing from the point where the force is applied to the axis of rotation.
E)points along the axis of rotation.

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Multiple Choice

Q 70Q 70

A force with a given magnitude is to be applied to a wheel.The torque can be maximized by:
A)applying the force near the axle, radially outward from the axle
B)applying the force near the rim, radially outward from the axle
C)applying the force near the axle, parallel to a tangent to the wheel
D)applying the force at the rim, tangent to the rim
E)applying the force at the rim, at 45 to the tangent

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Multiple Choice

Q 71Q 71

The meter stick shown below rotates about an axis through the point marked , 20 cm from one end.Five forces act on the stick: one at each end, one at the pivot point, and two 40 cm from one end, as shown.The magnitudes of the forces are all the same.Rank the forces according to the magnitudes of the torques they produce about the pivot point, least to greatest.
A), , , ,
B)and tie, then , ,
C)and tie, then , ,
D), , , and tie, then
E)and tie, then , then and tie

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Multiple Choice

Q 72Q 72

A disk is free to rotate on a fixed axis.A force of given magnitude F, in the plane of the disk, is to be applied.Of the following alternatives the greatest angular acceleration is obtained if the force is:
A)applied tangentially halfway between the axis and the rim
B)applied tangentially at the rim
C)applied radially halfway between the axis and the rim
D)applied radially at the rim
E)applied at the rim but neither radially nor tangentially

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Multiple Choice

Q 73Q 73

A force is applied to a billiard ball.In order to calculate the torque created by the force, you also need to know:
A)the mass of the ball
B)the rotational inertia of the ball
C)the kinetic energy of the ball
D)the angular speed of the ball
E)the location and orientation of the axis of rotation of the ball

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Multiple Choice

Q 74Q 74

The figure shows forces acting on a meter stick, which is constrained to rotate around the axis indicated by the dot Which force(s)create a positive torque around that axis?
A)only
B)and
C)only
D), and
E)only

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Multiple Choice

Q 75Q 75

A rod is pivoted about its center.A 5-N force is applied 4 m from the pivot and another 5-N force is applied 2 m from the pivot, as shown.The magnitude of the total torque about the pivot is:
A)0 Nm
B)5.0 Nm
C)8.7 Nm
D)15 Nm
E)26 Nm

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Multiple Choice

Q 76Q 76

A meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark.A horizontal force is applied perpendicularly to the end of the stick at 0 cm, as shown.A second horizontal force (not shown)is applied at the 100-cm end of the stick.If the stick does not rotate:
A)for all orientations of
B)for all orientations of
C)for all orientations of
D)for some orientations of and for others
E)for some orientations of and for others

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Multiple Choice

Q 77Q 77

= Ifor an object rotating about a fixed axis, where is the net torque acting on it, I is its rotational inertia, and is its angular acceleration.This expression:
A)is the definition of torque
B)is the definition of rotational inertia
C)is the definition of angular acceleration
D)follows directly from Newton's second law
E)depends on a principle of physics that is unrelated to Newton's second law

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Multiple Choice

Q 78Q 78

A uniform disk, a thin hoop, and a uniform solid sphere, all with the same mass and same outer radius, are each free to rotate about a fixed axis through its center.Assume the hoop is connected to the rotation axis by light spokes.With the objects starting from rest, identical forces are simultaneously applied to the rims, as shown.Rank the objects according to their angular velocities after a given time t, least to greatest.
A)disk, hoop, sphere
B)disk, sphere, hoop
C)hoop, sphere, disk
D)hoop, disk, sphere
E)sphere, disk, hoop

Free

Multiple Choice

Q 79Q 79

A cylinder is 0.10 m in radius and 0.20 m in length.Its rotational inertia, about the cylinder axis on which it is mounted, is 0.020 kg m

^{2}.A string is wound around the cylinder and pulled with a force of 1.0 N.The angular acceleration of the cylinder is: A)2.5 rad/s^{2}B)5.0 rad/s^{2}C)10 rad/s^{2}D)15 rad/s^{2}E)20 rad/s^{2}Free

Multiple Choice

Q 80Q 80

A disk with a rotational inertia of 2.0 kgm

^{2}and a radius of 0.40 m rotates on a frictionless fixed axis perpendicular to the disk faces and through its center.A force of 5.0 N is applied tangentially to the rim.The angular acceleration of the disk is: A)0.40 rad/s^{2}B)0.60 rad/s^{2}C)1.0 rad/s^{2}D)2.5 rad/s^{2}E)10 rad/s^{2}Free

Multiple Choice

Q 81Q 81

A disk with a rotational inertia of 5.0 kgm

^{2}and a radius of 0.25 m rotates on a frictionless fixed axis perpendicular to the disk and through its center.A force of 8.0 N is applied along the rotation axis.The angular acceleration of the disk is: A)0 rad/s^{2}B)0.40 rad/s^{2}C)0.60 rad/s^{2}D)1.0 rad/s^{2}E)2.5 rad/s^{2}Free

Multiple Choice

Q 82Q 82

A disk with a rotational inertia of 5.0 kg m

^{2}and a radius of 0.25 m rotates on a frictionless fixed axis perpendicular to the disk and through its center.A force of 8.0 N is applied tangentially to the rim.If the disk starts at rest, then after it has turned through half a revolution its angular velocity is: A)0.57 rad/s B)0.64 rad/s C)0.80 rad/s D)1.6 rad/s E)3.2 rad/sFree

Multiple Choice

Q 83Q 83

A thin circular hoop of mass 1.0 kg and radius 2.0 m is rotating about an axis through its center and perpendicular to its plane.It is slowing down at the rate of 7.0 rad/s

^{2}.The net torque acting on it is: A)7.0 N∙m B)14 N∙m C)28 N∙m D)44 N∙m E)none of theseFree

Multiple Choice

Q 84Q 84

A certain wheel has a rotational inertia of 12 kg∙m

^{2}.As it turns through 5.0 rev its angular velocity increases from 5.0 rad/s to 6.0 rad/s.If the net torque is constant its value is: A)0.015 N∙m B)0.18 N∙m C)0.57 N∙m D)2.1 N∙m E)13 N∙mFree

Multiple Choice

Q 85Q 85

An 8.0-cm radius disk with a rotational inertia of 0.12 kg∙m

^{2}is free to rotate on a horizontal axis.A string is fastened to the surface of the disk and a 10-kg mass hangs from the other end.The mass is raised by using a crank to apply a 9.0-Nm torque to the disk.The acceleration of the mass is: A)0.50 m/s^{2}B)3.9 m/s^{2}C)6.0 m/s^{2}D)12 m/s^{2}E)20 m/s^{2}Free

Multiple Choice

Q 86Q 86

A 16 kg block is attached to a cord that is wrapped around the rim of a flywheel of diameter 0.40 m and hangs vertically, as shown.The rotational inertia of the flywheel is 0.50 kg∙m

^{2}.When the block is released and the cord unwinds, the acceleration of the block is: A)0.15 g B)0.56 g C)0.84 g D)1.0 g E)1.3 gFree

Multiple Choice

Q 87Q 87

A 0.70-kg disk with a rotational inertia given by MR

^{2}/2 is free to rotate on a fixed horizontal axis suspended from the ceiling.A string is wrapped around the disk and a 2.0-kg mass hangs from the free end.If the string does not slip then as the mass falls and the cylinder rotates the suspension holding the cylinder pulls up on the mass with a force of: A)6.9 N B)9.8 N C)16 N D)26 N E)29 NFree

Multiple Choice

Q 88Q 88

A small disk of radius R

_{1}is mounted coaxially with a larger disk of radius R_{2}.The disks are securely fastened to each other and the combination is free to rotate on a fixed axle that is perpendicular to a horizontal frictionless table top, as shown in the overhead view below.The rotational inertia of the combination is I.A string is wrapped around the larger disk and attached to a block of mass m, on the table.Another string is wrapped around the smaller disk and is pulled with a force as shown.The acceleration of the block is: A)R_{1}F/mR_{2}B)R_{1}R_{2}F/(I - mR_{2}^{2}) C)R_{1}R_{2}F/(I + mR_{2}^{2}) D)R_{1}R_{2}F/(I - mR_{1}R_{2}) E)R_{1}R_{2}F/(I + mR_{1}R_{2})Free

Multiple Choice

Q 89Q 89

A small disk of radius R

_{1}is fastened coaxially to a larger disk of radius R_{2}.The combination is free to rotate on a fixed axle, which is perpendicular to a horizontal frictionless table top, as shown in the overhead view below.The rotational inertia of the combination is I.A string is wrapped around the larger disk and attached to a block of mass m, on the table.Another string is wrapped around the smaller disk and is pulled with a force as shown.The tension in the string pulling the block is: A)R_{1}F/R_{2}B)mR_{1}R_{2}F/(I - mR_{2}^{2}) C)mR_{1}R_{2}F/(I + mR_{2}^{2}) D)mR_{1}R_{2}F/(I - mR_{1}R_{2}) E)mR_{1}R_{2}F/(I + mR_{1}R_{2})Free

Multiple Choice

Q 90Q 90

A block is attached to each end of a rope that passes over a pulley suspended from the ceiling.The blocks do not have the same mass.If the rope does not slip on the pulley, then at any instant after the blocks start moving, the rope:
A)pulls on both blocks, but exerts a greater force on the heavier block
B)pulls on both blocks, but exerts a greater force on the lighter block
C)pulls on both blocks and exerts the same magnitude force on both blocks
D)does not pull on either block
E)pulls only on the lighter block

Free

Multiple Choice

Q 91Q 91

A disk with a rotational inertia of 5.0 kg∙m

^{2}and a radius of 0.25 m rotates on a fixed axis perpendicular to the disk and through its center.A force of 2.0 N is applied tangentially to the rim.As the disk turns through half a revolution the work done by the force is: A)1.6 J B)2.5 J C)6.3 J D)10 J E)40 JFree

Multiple Choice

Q 92Q 92

A circular saw is powered by a motor.When the saw is used to cut wood, the wood exerts a torque of 0.80 N∙m on the saw blade.If the blade rotates with a constant angular velocity of 20 rad/s the work done on the blade by the motor in 1.0 min is:
A)0 J
B)480 J
C)960 J
D)1500 J
E)1800 J

Free

Multiple Choice

Q 93Q 93

A disk has a rotational inertia of 6.0 kg∙m

^{2}and a constant angular acceleration of 2.0 rad/s^{2}.If it starts from rest the work done during the first 5.0 s by the net torque acting on it is: A)0 J B)30 J C)60 J D)300 J E)600 JFree

Multiple Choice

Q 94Q 94

A disk starts from rest and rotates around a fixed axis, subject to a constant net torque.The work done by the torque during the second 5 s is ______ as the work done during the first 5 s.
A)the same
B)half as much
C)twice as much
D)three times as much
E)four times as much

Free

Multiple Choice

Q 95Q 95

A disk starts from rest and rotates about a fixed axis, subject to a constant net torque.The work done by the torque during the second revolution is ______ as the work done during the first revolution.
A)the same
B)twice as much
C)half as much
D)four times as much
E)one fourth as much

Free

Multiple Choice

Q 96Q 96

A torque of 170 N∙m does 4700 J of work on a rotating flywheel.If the flywheel's initial kinetic energy is 1500 J, what is its final kinetic energy?
A)1500 J
B)3200 J
C)4700 J
D)6200 J
E)cannot be calculated without knowing the rotational inertia of the flywheel

Free

Multiple Choice

Q 97Q 97

A constant torque of 260 N∙m acts on a flywheel.If the flywheel makes 25 complete revolutions, how much work has been done by the torque on the flywheel?
A)1.7 J
B)41 J
C)600 J
D)6.5 x 10

^{3}J E)4.1 x 10^{4}JFree

Multiple Choice

Q 98Q 98

A constant torque of 260 N∙m acts on a flywheel.If the flywheel makes 25 complete revolutions in 2 minutes, what is the power exerted by the torque?
A)54 W
B)200 W
C)340 W
D)3.3 x 10

^{3}W E)2.0 x 10^{4}WFree

Multiple Choice

Q 99Q 99

A torque of 470 N∙m acts on a flywheel.At the instant that the flywheel's angular speed is 56 rad/s, at what rate is work being done by the torque?
A)8.4 W
B)26 W
C)112 W
D)4200 W
E)2.6 x 10

^{4}WFree

Multiple Choice