Question 1

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?

Accepted Answer

A) 0.86 rad/s2 
B) 0.74 rad/s2 
C) 0.37 rad/s2 
D) 11 rad/s2 
E) 1.2 rad/s2

Question 2

A hoop with a mass of 2.75 kg is rolling without slipping along a horizontal surface with a speed of 4.5 m/s when it starts down a ramp that makes an angle of 25° below the horizontal.What is the rotational kinetic energy of the hoop after it has rolled 3.0 m down as measured along the surface of the ramp?

Accepted Answer

A) 34 J 
B) 22 J 
C) 45 J 
D) 62 J 
E) This question cannot be answered without knowing the radius of the hoop.

Question 3

A pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41 rad/s2.Through what angle does the pulley turn in 5.26 s?

Accepted Answer

A) 113 rad 
B) 22.6 rad 
C) 42.6 rad 
D) 19.3 rad 
E) 160 rad

Question 4

A wheel accelerates from rest to 
At a uniform rate of 
Through what angle (in radians)did the wheel turn while accelerating?

Accepted Answer

A) 30 rad 
B) 24 rad 
C) 60 rad 
D) 38 rad

Question 5

At a certain instant,a compact disc is rotating at 210 rpm.What is its angular speed in rad/s?

Accepted Answer

A) 11 rad/s 
B) 22 rad/s 
C) 45 rad/s 
D) 69 rad/s 
E) 660 rad/s

Question 6

An electrical motor spins at a constant 
If the rotor radius is 
What is the linear acceleration of the edge of the rotor?

Accepted Answer

A) 5,707 m/s2 
B) 281.6 m/s2 
C) 572,400 m/s2 
D) 28.20 m/s2

Question 7

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?

Accepted Answer

A) 4.13 s 
B) 2.07 s 
C) 118 s 
D) 4.77 s 
E) 8.26 s

Question 8

What is the angular speed,in rad/s,of a flywheel turning at 813.0 rpm?

Accepted Answer

A) 85.14 rad/s 
B) 13.53 rad/s 
C) 63.84 rad/s 
D) 95.33 rad/s

Question 9

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?

Accepted Answer

A) 2.34 rad/s2 
B) 5.46 rad/s2 
C) 6.50 rad/s2 
D) 8.35 rad/s2 
E) 10.9 rad/s2

Question 10

A solid uniform sphere of mass 120 kg and radius 1.7 m starts from rest and rolls without slipping down an inclined plane of vertical height 5.3 m.What is the angular speed of the sphere at the bottom of the inclined plane?

Accepted Answer

A) 5.1 rad/s 
B) 8.7 rad/s 
C) 9.7 rad/s 
D) 6.1 rad/s

Question 11

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?

Accepted Answer

A) 1.8 kg ∙ m2 
B) 1.5 kg ∙ m2 
C) 0.40 kg ∙ m2 
D) 2.5 kg ∙ m2

Question 12

Two uniform solid balls,one of radius R and mass M,the other of radius 2R and mass 8M,roll down a high incline.They start together from rest at the top of the incline.Which one will reach the bottom of the incline first?

Accepted Answer

A) The small sphere arrives first. 
B) Both reach the bottom at the same time. 
C) The large sphere arrives first.

Question 13

While spinning down from 500 rpm to rest,a flywheel does 
Of work.This flywheel is in the shape of a solid uniform disk of radius 1.2 m.What is the mass of this flywheel?

Accepted Answer

A) 4.0 kg 
B) 3.4 kg 
C) 4.6 kg 
D) 5.2 kg

Question 14

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/s2.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?

Accepted Answer

A) 8.05 m/s2 
B) 7.27 m/s2 
C) 2.58 m/s2 
D) 3.46 m/s2 
E) 4.10 m/s2

Question 15

To drive a typical car at 40 mph on a level road for one hour requires about 3.2 × 107 J of energy.Suppose we tried to store this much energy in a spinning,solid,uniform,cylindrical flywheel.A large flywheel cannot be spun too fast or it will fracture.If we used a flywheel of diameter 1.2 m and mass 400 kg,what angular speed would be required to store 3.2 × 107 J?

Accepted Answer

A) 1800 rad/s 
B) 3600 rad/s 
C) 940 rad/s 
D) 530 rad/s 
E) 5500 rad/s

Question 16

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?

Accepted Answer

A) 1.8 rad/s2 
B) 0.90 rad/s2 
C) 5.7 rad/s2 
D) 11 rad/s2

Question 17

An Atwood machine consists of a mass of 3.5 kg connected by a light string to a mass of 6.0 kg over a frictionless pulley with a moment of inertia of 0.0352 kg ∙ m2 and a radius of 12.5 cm.If the system is released from rest,what is the speed of the masses after they have moved through 1.25 m if the string does not slip on the pulley?

Accepted Answer

A) 2.0 m/s 
B) 2.3 m/s 
C) 4.0 m/s 
D) 5.0 m/s 
E) 6.0 m/s

Question 18

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?

Accepted Answer

A) 100 rad/s 
B) 50 rad/s 
C) 25 rad/s 
D) 20 rad/s 
E) 10 rad/s

Question 19

A small uniform disk and a small uniform sphere are released simultaneously at the top of a high inclined plane,and they roll down without slipping.Which one will reach the bottom first?

Accepted Answer

A) the one of smallest diameter 
B) the one of greatest mass 
C) the disk 
D) the sphere 
E) They will reach the bottom at the same time.

Question 20

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?

Accepted Answer

A) 64 s 
B) 62 s 
C) 66 s 
D) 68 s 
E) 70 s

Exam 10: Rotational Kinematics and Energy

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 pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41 rad/s².Through what angle does the pulley turn in 5.26 s?

A wheel accelerates from rest to At a uniform rate of Through what angle (in radians) did the wheel turn while accelerating?