Question 1

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

Accepted Answer

A) 4$\pi$2 rad/s2 
B) 2$\pi$rad/s2 
C) 1/30 rad/s2 
D) 2$\pi$/30 rad/s2 
E) 4$\pi$ rad/s2 
A) 4$\pi$2 rad/s2 
B) 2$\pi$rad/s2 
C) 1/30 rad/s2 
D) 2$\pi$/30 rad/s2 
E) 4$\pi$ rad/s2

Question 2

This graph shows the angular velocity of a turntable as a function of time.What is its angular acceleration at t = 3.5 s?

Accepted Answer

A) −10 rad/s2  
B) −5 rad/s2 
C) 0 rad/s2 
D) 5 rad/s2 
E) 10 rad/s2 
A) −10 rad/s2  
B) −5 rad/s2 
C) 0 rad/s2 
D) 5 rad/s2 
E) 10 rad/s2

Question 3

The magnitude of the acceleration of a point on a spinning wheel is increased by a factor of 4 if:

Accepted Answer

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 
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

Question 4

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:

Accepted Answer

A) 4.0 kg∙m2 
B) 12 kg∙m2 
C) 9.6 kg∙m2 
D) 4.8 kg∙m2 
E) none of these 
A) 4.0 kg∙m2 
B) 12 kg∙m2 
C) 9.6 kg∙m2 
D) 4.8 kg∙m2 
E) none of these

Question 5

A wheel starts from rest and has an angular acceleration of 4.0 rad/s2.When it has made 10 rev its angular velocity is:

Accepted Answer

A) 8.9 rad/s 
B) 16 rad/s 
C) 22 rad/s 
D) 32 rad/s 
E) 250 rad/s 
A) 8.9 rad/s 
B) 16 rad/s 
C) 22 rad/s 
D) 32 rad/s 
E) 250 rad/s

Question 6

A force is applied to a billiard ball.In order to calculate the torque created by the force, you also need to know:

Accepted Answer

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 
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

Question 7

If a wheel turning at a constant rate completes 100 revolutions in 10 s its angular speed is:

Accepted Answer

A) 0.31 rad/s 
B) 0.63 rad/s 
C) 10 rad/s 
D) 31 rad/s 
E) 63 rad/s 
A) 0.31 rad/s 
B) 0.63 rad/s 
C) 10 rad/s 
D) 31 rad/s 
E) 63 rad/s

Question 8

The angular velocity of a rotating turntable is given in rad/s by ω(t)= 4.5 + 0.64t - 2.7t2.What is its average angular acceleration between t = 1.0 s and t = 3.0 s?

Accepted Answer

A) 0.64 rad/s2 
B) −5.4 rad/s2 
C) −7.7 rad/s2 
D) −10 rad/s2 
E) −27 rad/s2 
A) 0.64 rad/s2 
B) −5.4 rad/s2 
C) −7.7 rad/s2 
D) −10 rad/s2 
E) −27 rad/s2

Question 9

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:

Accepted Answer

A) 3.3 rad/s 
B) 4.4 rad/s 
C) 6.7 rad/s 
D) 11 rad/s 
E) 48 rad/s 
A) 3.3 rad/s 
B) 4.4 rad/s 
C) 6.7 rad/s 
D) 11 rad/s 
E) 48 rad/s

Question 10

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?

Accepted Answer

A) 8.4 W 
B) 26 W 
C) 112 W 
D) 4200 W 
E) 2.6 x 104 W 
A) 8.4 W 
B) 26 W 
C) 112 W 
D) 4200 W 
E) 2.6 x 104 W

Question 11

The angular speed of the minute hand of a watch is:

Accepted Answer

A) (60/$\pi$)rad/s 
B) (1800/$\pi$)rad/s 
C) ($\pi$)rad/s 
D) ($\pi$/1800)rad/s 
E) ($\pi$/60)rad/s 
A) (60/$\pi$)rad/s 
B) (1800/$\pi$)rad/s 
C) ($\pi$)rad/s 
D) ($\pi$/1800)rad/s 
E) ($\pi$/60)rad/s

Question 12

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?

Accepted Answer

A) 1500 J 
B) 3200 J 
C) 4700 J 
D) 6200 J 
E) cannot be calculated without knowing the rotational inertia of the flywheel 
A) 1500 J 
B) 3200 J 
C) 4700 J 
D) 6200 J 
E) cannot be calculated without knowing the rotational inertia of the flywheel

Question 13

If a wheel turns with constant angular speed then:

Accepted Answer

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 
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

Question 14

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

Accepted Answer

A) MR2/2 
B) ML2/2 
C) ML2 
D) MR2 
E) none of these 
A) MR2/2 
B) ML2/2 
C) ML2 
D) MR2 
E) none of these

Question 15

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:

Accepted Answer

A) 1 
B) 2 
C) 1/2 
D) 4 
E) 1/4 
A) 1 
B) 2 
C) 1/2 
D) 4 
E) 1/4

Question 16

A small disk of radius R1 is fastened coaxially to a larger disk of radius R2.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:

Accepted Answer

A) R1F/R2 
B) mR1R2F/(I - mR22) 
C) mR1R2F/(I + mR22) 
D) mR1R2F/(I - mR1R2) 
E) mR1R2F/(I + mR1R2) 
A) R1F/R2 
B) mR1R2F/(I - mR22) 
C) mR1R2F/(I + mR22) 
D) mR1R2F/(I - mR1R2) 
E) mR1R2F/(I + mR1R2)

Question 17

for an object rotating about a fixed axis, where     is the net torque acting on it, I is its rotational inertia, and  $\alpha$ is its angular acceleration.This expression:

Accepted Answer

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 
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

Question 18

A disk with a rotational inertia of 5.0 kg.m2 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:

Accepted Answer

A) 0 rad/s2 
B) 0.40 rad/s2 
C) 0.60 rad/s2 
D) 1.0 rad/s2 
E) 2.5 rad/s2 
A) 0 rad/s2 
B) 0.40 rad/s2 
C) 0.60 rad/s2 
D) 1.0 rad/s2 
E) 2.5 rad/s2

Question 19

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.

Accepted Answer

A) 1, 2, 3 
B) 3, 2, 1 
C) 3, then 1 and 2 tie 
D) 1, 3, 2 
E) All are the same 
A) 1, 2, 3 
B) 3, 2, 1 
C) 3, then 1 and 2 tie 
D) 1, 3, 2 
E) All are the same

Question 20

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:

Accepted Answer

A) 0 N.m 
B) 5.0 N.m 
C) 8.7 N.m 
D) 15 N.m 
E) 26 N.m 
A) 0 N.m 
B) 5.0 N.m 
C) 8.7 N.m 
D) 15 N.m 
E) 26 N.m

Exam 10: Rotation

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

This graph shows the angular velocity of a turntable as a function of time.What is its angular acceleration at t = 3.5 s?

The magnitude of the acceleration of a point on a spinning wheel is increased by a factor of 4 if:

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 wheel starts from rest and has an angular acceleration of 4.0 rad/s2.When it has made 10 rev its angular velocity is:

A force is applied to a billiard ball.In order to calculate the torque created by the force, you also need to know:

If a wheel turning at a constant rate completes 100 revolutions in 10 s its angular speed is:

The angular velocity of a rotating turntable is given in rad/s by ω(t)= 4.5 + 0.64t - 2.7t2.What is its average angular acceleration between t = 1.0 s and t = 3.0 s?

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 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?

The angular speed of the minute hand of a watch is:

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?

If a wheel turns with constant angular speed then:

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

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:

for an object rotating about a fixed axis, where is the net torque acting on it, I is its rotational inertia, and α\alphaα is its angular acceleration.This expression:

A disk with a rotational inertia of 5.0 kg.m2 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:

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 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:

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A wheel starts from rest and has an angular acceleration of 4.0 rad/s².When it has made 10 rev its angular velocity is:

The angular velocity of a rotating turntable is given in rad/s by ω(t)= 4.5 + 0.64t - 2.7t².What is its average angular acceleration between t = 1.0 s and t = 3.0 s?

A disk with a rotational inertia of 5.0 kg.m² 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: