Question 1

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

Question 2

Two solid balls (one large,the other small)and a cylinder roll down a hill.Which has the greatest speed at the bottom and which the least?

Accepted Answer

A) The large ball has the greatest; the small ball has the least. 
B) The small ball has the greatest; the large ball has the least. 
C) The cylinder has the greatest; the small ball has the least. 
D) The cylinder has the greatest; both balls have the same lesser speed. 
E) Both balls have the same greater speed; the cylinder has the least. 
A) The large ball has the greatest; the small ball has the least. 
B) The small ball has the greatest; the large ball has the least. 
C) The cylinder has the greatest; the small ball has the least. 
D) The cylinder has the greatest; both balls have the same lesser speed. 
E) Both balls have the same greater speed; the cylinder has the least.

Question 3

The Empire's space station is a long way from any star.It is circular and has a radius of 5.10 km.The angular velocity that is needed to give the station an artificial gravity of 9.80 m/s2 at its circumference is

Accepted Answer

A) 4.4 $\times$ 10-2 rad/s 
B) 7.0 $\times$ 10-3 rad/s 
C) 0.28 rad/s 
D) - 0.22 rad/s 
E) 1.3 $\times$ 103 rad/s 
A) 4.4 $\times$ 10-2 rad/s 
B) 7.0 $\times$ 10-3 rad/s 
C) 0.28 rad/s 
D) - 0.22 rad/s 
E) 1.3 $\times$ 103 rad/s

Question 4

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 
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 5

When an object is moving in a circle at constant speed,its acceleration is

Accepted Answer

A) constantly increasing. 
B) constant in direction. 
C) zero. 
D) constant in magnitude. 
E) constant in both magnitude and direction. 
A) constantly increasing. 
B) constant in direction. 
C) zero. 
D) constant in magnitude. 
E) constant in both magnitude and direction.

Question 6

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

Question 7

Power can be expressed as the product of

Accepted Answer

A) force and displacement. 
B) torque and angular displacement. 
C) torque and angular acceleration. 
D) force and acceleration. 
E) torque and angular velocity. 
A) force and displacement. 
B) torque and angular displacement. 
C) torque and angular acceleration. 
D) force and acceleration. 
E) torque and angular velocity.

Question 8

A point P is at a distance R from the axis of rotation of a rigid body.The linear speed,centripetal acceleration,and tangential acceleration of the point can be expressed as

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

A solid disk (I =   MR2)that is 10 cm in diameter has a mass of 4 kg.The force applied at the outer surface required to produce an angular acceleration of 6 rad/s2 about an axis through the center of the disc is

Accepted Answer

A) 0.24 kN 
B) 0.12 kN 
C) 0.30 N 
D) 0.60 N 
E) 1.2 N 
A) 0.24 kN 
B) 0.12 kN 
C) 0.30 N 
D) 0.60 N 
E) 1.2 N

Question 10

Use the figure on the below to answer the next 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 
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 11

To increase the moment of inertia of a body about an axis,you must

Accepted Answer

A) increase the angular acceleration. 
B) increase the angular velocity. 
C) decrease the angular velocity. 
D) make the body occupy less space. 
E) place part of the body farther from the axis. 
A) increase the angular acceleration. 
B) increase the angular velocity. 
C) decrease the angular velocity. 
D) make the body occupy less space. 
E) place part of the body farther from the axis.

Question 12

Four 50-g point masses are at the corners of a square with 20-cm sides.What is the moment of inertia of this system about an axis perpendicular to the plane of the square and passing through its center?

Accepted Answer

A) 1.0 $\times$ 10-3 kg · m2  
B) 4.0 $\times$ 10-3 kg · m2  
C) 2.0 $\times$ 10-3 kg · m2  
D) 8.0 $\times$ 10-3 kg · m2  
E) 2.8 $\times$ 10-3 kg · m2  
A) 1.0 $\times$ 10-3 kg · m2  
B) 4.0 $\times$ 10-3 kg · m2  
C) 2.0 $\times$ 10-3 kg · m2  
D) 8.0 $\times$ 10-3 kg · m2  
E) 2.8 $\times$ 10-3 kg · m2

Question 13

Two masses M and m (M > m)are hung over a disc (Idisc =   M'R2)and are released so that they accelerate.If T1 is the tension in the cord on the left and T2 is the tension in the cord on the right,then

Accepted Answer

A) T1 = T2  
B) T2 > T1  
C) T2 1  
D) T2 = Mg 
E) T2 = Mg/m 
A) T1 = T2  
B) T2 > T1  
C) T2 1  
D) T2 = Mg 
E) T2 = Mg/m

Question 14

A ball of mass m1,connected to another mass m2 by a string,is whirled at a constant speed in a horizontal circle of radius R equal to 0.800m.If the mass m2 = 5.00 kg,the kinetic energy of the ball is

Accepted Answer

A) 0.981 J 
B) 2.45 J 
C) 4.90 J 
D) 19.6 J 
E) 39.2 J 
A) 0.981 J 
B) 2.45 J 
C) 4.90 J 
D) 19.6 J 
E) 39.2 J

Question 15

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

Question 16

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 
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 17

A solid cylinder of mass m = 3 kg and radius r = 12 cm is initially rotating about its central axis with angular frequency $\omega$ = 25 radians/s.How many revolutions does it make after a retarding force of 0.5 N is applied to the outer surface?

Accepted Answer

A) 0.018 rev 
B) 0.11 rev 
C) 0.036 rev 
D) 0.0090 rev 
E) 0.072 rev 
A) 0.018 rev 
B) 0.11 rev 
C) 0.036 rev 
D) 0.0090 rev 
E) 0.072 rev

Question 18

A cylinder (I = ½mR2)rolls along a level floor with a speed v.The work required to stop this cylinder is

Accepted Answer

A) ¼ mv2  
B) ½ mv2  
C) ¾ mv2  
D) mv2  
E) 1.25mv2  
A) ¼ mv2  
B) ½ mv2  
C) ¾ mv2  
D) mv2  
E) 1.25mv2

Question 19

The ball shown in the figure will loop-the-loop if it starts from a point high enough on the incline.When the ball is at point A,the centripetal force on it is best represented by which of the following vectors?

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 20

A solid cylinder has a moment of inertia of 2 kg · m2.It is at rest at time zero when a net torque given by   is applied.After 2 s,the angular velocity of the cylinder will be

Accepted Answer

A) 3.0 rad/s 
B) 12 rad/s 
C) 14 rad/s 
D) 24 rad/s 
E) 28 rad/s 
A) 3.0 rad/s 
B) 12 rad/s 
C) 14 rad/s 
D) 24 rad/s 
E) 28 rad/s

Exam 9: Rotation

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

Two solid balls (one large,the other small)and a cylinder roll down a hill.Which has the greatest speed at the bottom and which the least?

The Empire's space station is a long way from any star.It is circular and has a radius of 5.10 km.The angular velocity that is needed to give the station an artificial gravity of 9.80 m/s2 at its circumference is

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

When an object is moving in a circle at constant speed,its acceleration 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

Power can be expressed as the product of

A point P is at a distance R from the axis of rotation of a rigid body.The linear speed,centripetal acceleration,and tangential acceleration of the point can be expressed as

A solid disk (I = MR2)that is 10 cm in diameter has a mass of 4 kg.The force applied at the outer surface required to produce an angular acceleration of 6 rad/s2 about an axis through the center of the disc is

Use the figure on the below to answer the next 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?

To increase the moment of inertia of a body about an axis,you must

Four 50-g point masses are at the corners of a square with 20-cm sides.What is the moment of inertia of this system about an axis perpendicular to the plane of the square and passing through its center?

Two masses M and m (M > m)are hung over a disc (Idisc = M'R2)and are released so that they accelerate.If T1 is the tension in the cord on the left and T2 is the tension in the cord on the right,then

A ball of mass m1,connected to another mass m2 by a string,is whirled at a constant speed in a horizontal circle of radius R equal to 0.800m.If the mass m2 = 5.00 kg,the kinetic energy of the ball is

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 solid cylinder of mass m = 3 kg and radius r = 12 cm is initially rotating about its central axis with angular frequency ω\omegaω = 25 radians/s.How many revolutions does it make after a retarding force of 0.5 N is applied to the outer surface?

A cylinder (I = ½mR2)rolls along a level floor with a speed v.The work required to stop this cylinder is

The ball shown in the figure will loop-the-loop if it starts from a point high enough on the incline.When the ball is at point A,the centripetal force on it is best represented by which of the following vectors?

A solid cylinder has a moment of inertia of 2 kg · m2.It is at rest at time zero when a net torque given by is applied.After 2 s,the angular velocity of the cylinder will be

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The Empire's space station is a long way from any star.It is circular and has a radius of 5.10 km.The angular velocity that is needed to give the station an artificial gravity of 9.80 m/s² at its circumference is

A solid disk (I = MR²)that is 10 cm in diameter has a mass of 4 kg.The force applied at the outer surface required to produce an angular acceleration of 6 rad/s² about an axis through the center of the disc is

Use the figure on the below to answer the next 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?

Two masses M and m (M > m)are hung over a disc (I_dis_c = M'R²)and are released so that they accelerate.If T₁ is the tension in the cord on the left and T₂ is the tension in the cord on the right,then

A ball of mass m₁,connected to another mass m₂ by a string,is whirled at a constant speed in a horizontal circle of radius R equal to 0.800m.If the mass m₂ = 5.00 kg,the kinetic energy of the ball is

A solid cylinder of mass m = 3 kg and radius r = 12 cm is initially rotating about its central axis with angular frequency $\omega$ = 25 radians/s.How many revolutions does it make after a retarding force of 0.5 N is applied to the outer surface?

A cylinder (I = ½mR²)rolls along a level floor with a speed v.The work required to stop this cylinder is

A solid cylinder has a moment of inertia of 2 kg · m².It is at rest at time zero when a net torque given by is applied.After 2 s,the angular velocity of the cylinder will be