Question 1

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?

Accepted Answer

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.

Question 2

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?

Accepted Answer

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.

Question 3

A wheel rotates with a constant nonzero angular acceleration. Which of the following quantities remains constant in magnitude?

Accepted Answer

A)   , tangential velocity 
B)   r, radial acceleration 
C)   t, tangential acceleration 
D)   , angular velocity 
E)  All of these are correct.

Question 4

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?

Accepted Answer

A)  vA = vB = vC  
B)  vA > vB; vA > vC  
C)  vA C; vB C  
D)  vA B; vB C  
E)  vA = vB; vB C

Question 5

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.

Accepted Answer

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 speeds

Question 6

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?

Accepted Answer

A)  24 N · m 
B)  2.5 N · m 
C)  80 N · m 
D)  2.4 $\times$ 103 N · m 
E)  49 N · m

Question 7

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.

Accepted Answer

A)  2.0 $\times$ 102 N 
B)  59 N 
C)  7.0 $\times$ 105 N 
D)  9.0 N 
E)  88 N

Question 8

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)

Accepted Answer

A)  5.6 cm/s 
B)  35 cm/s 
C)  3.3 $\times$ 102 cm/s 
D)  21 m/s 
E)  18 cm/s

Question 9

Use the figure the problem.
A mass m = 0.5 kg is hung from a pulley with moment of inertia I = 0.20kg.mS1U1P12S1S1P0 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?

Accepted Answer

A)  0.5 N.m 
B)  0.9 N.m 
C)  2.9 N.m 
D)  3.9 N.m 
E)  4.5 N.m

Question 10

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

Accepted Answer

A)  4.4 m/s 
B)  9.8 m/s 
C)  14 m/s 
D)  98 m/s 
E)  0.44 km/s

Question 11

Two blocks m1 (= 0.4 kg) and m2 (= 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 m1 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.

Accepted Answer

A)  0.64 
B)  1.4 
C)  1.6 
D)  0.74 
E)  1.8

Question 12

A body that moves with a constant speed in a circle

Accepted Answer

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.

Question 13

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

Accepted Answer

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

Question 14

The moment of inertia of a slim rod about a transverse axis through one end is mL2/3, 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

Accepted Answer

A)  0.14 kg · m2  
B)  20 kg · m2  
C)  0.020 kg · m2  
D)  80 kg · m2  
E)  4.5 kg · m2

Question 15

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

Accepted Answer

A)  82.2 N · m 
B)  157 N · m 
C)  225 N · m 
D)  392 N · m 
E)  461 N · m

Question 16

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?

Accepted Answer

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.

Question 17

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?

Accepted Answer

A)  20 
B)  40 
C)  60 
D)  80 
E)  100

Question 18

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

Accepted Answer

A)  36 m/s 
B)  3.6 m/s 
C)  72 m/s 
D)  18 m/s 
E)  98 m/s

Question 19

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

Accepted Answer

A)  equal to R$\omega$ in the direction of motion of the center of mass. 
B)  equal to R$\omega$ 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.

Question 20

Two small masses, mA = 4.0 $\times$ 10-3 kg and mB = 2.0 $\times$ 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

Accepted Answer

A)  4.0 rad/s2  
B)  2.7 rad/s2  
C)  11 rad/s2  
D)  12 rad/s2  
E)  4.0 $\times$ 102 rad/s2

Exam 9: Rotation

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 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 wheel rotates with a constant nonzero angular acceleration. Which of the following quantities remains constant in magnitude?

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 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 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.

Use the figure the problem. A mass m = 0.5 kg is hung from a pulley with moment of inertia I = 0.20kg.m² 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 body that moves with a constant speed in a circle

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

The moment of inertia of a slim rod about a transverse axis through one end is mL²/3, 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 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

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 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 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 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

Exam 9: Rotation

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 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 wheel rotates with a constant nonzero angular acceleration. Which of the following quantities remains constant in magnitude?

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 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 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 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)

Use the figure the problem. A mass m = 0.5 kg is hung from a pulley with moment of inertia I = 0.20kg.m2 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 body that moves with a constant speed in a circle

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

The moment of inertia of a slim rod about a transverse axis through one end is mL2/3, 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 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

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 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 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 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

Two small masses, mA = 4.0 ×\times× 10-3 kg and mB = 2.0 ×\times× 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

Use the figure the problem. A mass m = 0.5 kg is hung from a pulley with moment of inertia I = 0.20kg.m² 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?

The moment of inertia of a slim rod about a transverse axis through one end is mL²/3, 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