Question 1

A solid uniform cylinder is rolling without slipping.What fraction of its kinetic energy is rotational?

Accepted Answer

A) 1/3 
B) 2/3 
C) 1/2 
D) 1/4 
E) 3/4 
A) 1/3 
B) 2/3 
C) 1/2 
D) 1/4 
E) 3/4

Question 2

As shown in the figure,two blocks are connected by a light string that passes over a frictionless pulley having a moment of inertia of 0.0040 kg ∙ m2 and diameter 10 cm.The coefficient of kinetic friction between the table top and the upper block is 0.30.The blocks are released from rest,and the string does not slip on the pulley.How fast is the upper block moving when the lower one has fallen 0.60 m?

Accepted Answer

A) 1.2 m/s 
B) 5.4 m/s 
C) 3.2 m/s 
D) 2.0 m/s 
E) 1.4 m/s 
A) 1.2 m/s 
B) 5.4 m/s 
C) 3.2 m/s 
D) 2.0 m/s 
E) 1.4 m/s

Question 3

A solid sphere,solid cylinder,and a hollow pipe all have equal masses and radii.If the three of them are released simultaneously at the top of an inclined plane and do not slip,which one will reach the bottom first?

Accepted Answer

A) sphere 
B) pipe 
C) cylinder 
D) The pipe and cylinder arrive together before the sphere. 
E) They all reach the bottom at the same time. 
A) sphere 
B) pipe 
C) cylinder 
D) The pipe and cylinder arrive together before the sphere. 
E) They all reach the bottom at the same time.

Question 4

Through how many degrees does a 33 rpm turntable rotate in

Accepted Answer

A) 63° 
B) 35° 
C) 46° 
D) 74° 
A) 63° 
B) 35° 
C) 46° 
D) 74°

Question 5

A solid sphere and a solid cylinder,both uniform and of the same mass and radius,roll without slipping at the same forward speed.It is correct to say that the total kinetic energy of the solid sphere is

Accepted Answer

A) more than the total kinetic energy of the cylinder. 
B) less than the total kinetic energy of the cylinder. 
C) equal to the total kinetic energy of the cylinder. 
A) more than the total kinetic energy of the cylinder. 
B) less than the total kinetic energy of the cylinder. 
C) equal to the total kinetic energy of the cylinder.

Question 6

A uniform ball is released from rest on a no-slip surface,as shown in the figure.After reaching its lowest point,the ball begins to rise again,this time on a frictionless surface.When the ball reaches its maximum height on the frictionless surface,it is

Accepted Answer

A) higher than when it was released. 
B) lower than when it was released. 
C) at the same height from which it was released. 
D) It is impossible to tell without knowing the mass of the ball. 
E) It is impossible to tell without knowing the radius of the ball. 
A) higher than when it was released. 
B) lower than when it was released. 
C) at the same height from which it was released. 
D) It is impossible to tell without knowing the mass of the ball. 
E) It is impossible to tell without knowing the radius of the ball.

Question 7

A uniform solid disk is released from rest and rolls without slipping down an inclined plane that makes an angle of 25° with the horizontal.What is the forward speed of the disk after it has rolled 3.0 m,measured along the plane?

Accepted Answer

A) 2.0 m/s 
B) 3.5 m/s 
C) 4.1 m/s 
D) 5.7 m/s 
E) 6.3 m/s 
A) 2.0 m/s 
B) 3.5 m/s 
C) 4.1 m/s 
D) 5.7 m/s 
E) 6.3 m/s

Question 8

When a rigid object rotates about a fixed axis,what is true about all the points in the object? (There could be more than one correct choice. )

Accepted Answer

A) They all have the same angular speed. 
B) They all have the same tangential speed. 
C) They all have the same angular acceleration. 
D) They all have the same tangential acceleration. 
E) They all have the same radial acceleration. 
A) They all have the same angular speed. 
B) They all have the same tangential speed. 
C) They all have the same angular acceleration. 
D) They all have the same tangential acceleration. 
E) They all have the same radial acceleration.

Question 9

A solid uniform disk of diameter 3.20 m and mass 42 kg rolls without slipping to the bottom of a hill,starting from rest.If the angular speed of the disk is 4.27 rad/s at the bottom,how high did it start on the hill?

Accepted Answer

A) 3.57 m 
B) 2.68 m 
C) 3.14 m 
D) 4.28 m 
A) 3.57 m 
B) 2.68 m 
C) 3.14 m 
D) 4.28 m

Question 10

A wheel having a moment of inertia of 5.00 kg ∙ m2 starts from rest and accelerates under a constant torque of 3.00 N ∙ m for 8.00 s.What is the wheel's rotational kinetic energy at the end of 8.00 s?

Accepted Answer

A) 57.6 J 
B) 64.0 J 
C) 78.8 J 
D) 122 J 
A) 57.6 J 
B) 64.0 J 
C) 78.8 J 
D) 122 J

Question 11

A solid uniform sphere is rolling without slipping along a horizontal surface with a speed of 5.5 m/s when it starts up a ramp that makes an angle of 25° with the horizontal.What is the speed of the sphere after it has rolled 3.0 m up as measured along the surface of the ramp?

Accepted Answer

A) 4.0 m/s 
B) 8.0 m/s 
C) 1.9 m/s 
D) 2.2 m/s 
E) 3.5 m/s 
A) 4.0 m/s 
B) 8.0 m/s 
C) 1.9 m/s 
D) 2.2 m/s 
E) 3.5 m/s

Question 12

Suppose a solid uniform sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest.The angular velocity of the sphere at the bottom of the incline depends on

Accepted Answer

A) the mass of the sphere. 
B) the radius of the sphere. 
C) both the mass and the radius of the sphere. 
D) neither the mass nor the radius of the sphere. 
A) the mass of the sphere. 
B) the radius of the sphere. 
C) both the mass and the radius of the sphere. 
D) neither the mass nor the radius of the sphere.

Question 13

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 forward speed of the hoop after it has rolled 3.0 m down as measured along the surface of the ramp?

Accepted Answer

A) 4.9 m/s 
B) 6.3 m/s 
C) 5.2 m/s 
D) 5.7 m/s 
E) 8.0 m/s 
A) 4.9 m/s 
B) 6.3 m/s 
C) 5.2 m/s 
D) 5.7 m/s 
E) 8.0 m/s

Question 14

A wheel rotates through an angle of 13.8 rad as it slows down uniformly from 22.0 rad/s to 13.5 rad/s.What is the magnitude of the angular acceleration of the wheel?

Accepted Answer

A) 0.616 rad/s2 
B) 5.45 rad/s2 
C) 111 rad/s2 
D) 22.5 rad/s2 
E) 10.9 rad/s2 
A) 0.616 rad/s2 
B) 5.45 rad/s2 
C) 111 rad/s2 
D) 22.5 rad/s2 
E) 10.9 rad/s2

Question 15

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 30 s,and then power is shut off.The wheel slows down uniformly at  
Until the wheel stops.What is the total number of revolutions made by the wheel in this situation?

Accepted Answer

A) 510 
B) 280 
C) 320 
D) 470 
E) 750 
A) 510 
B) 280 
C) 320 
D) 470 
E) 750

Question 16

A string is wrapped tightly around a fixed pulley that has a moment of inertia of 0.0352 kg ∙ m2 and a radius of 12.5 cm.A mass of 423 g is attached to the free end of the string.With the string vertical and taut,the mass is gently released so it can descend under the influence of gravity.As the mass descends,the string unwinds and causes the pulley to rotate,but does not slip on the pulley.What is the speed of the mass after it has fallen through 1.25 m?

Accepted Answer

A) 2.00 m/s 
B) 2.28 m/s 
C) 1.97 m/s 
D) 3.94 m/s 
E) 4.95 m/s 
A) 2.00 m/s 
B) 2.28 m/s 
C) 1.97 m/s 
D) 3.94 m/s 
E) 4.95 m/s

Question 17

A hoop is rolling without slipping along a horizontal surface with a forward speed of 5.50 m/s when it starts up a ramp that makes an angle of 25.0° with the horizontal.What is the speed of the hoop after it has rolled 3.00 m up as measured along the surface of the ramp?

Accepted Answer

A) 4.22 m/s 
B) 1.91 m/s 
C) 2.06 m/s 
D) 3.79 m/s 
E) 8.02 m/s 
A) 4.22 m/s 
B) 1.91 m/s 
C) 2.06 m/s 
D) 3.79 m/s 
E) 8.02 m/s

Question 18

What is the kinetic energy of a 120-cm thin uniform rod with a mass of 450 g that is rotating about its center at 3.60 rad/s?

Accepted Answer

A) 0.350 J 
B) 4.20 J 
C) 0.700 J 
D) 0.960 J 
E) 2.10 J 
A) 0.350 J 
B) 4.20 J 
C) 0.700 J 
D) 0.960 J 
E) 2.10 J

Question 19

A pencil that is 15.7 cm long is released from a vertical position with the eraser end resting on a table.The eraser does not slip as it tips over.Treat the pencil like a uniform rod.What is the angular speed of the pencil just before it hits the table?

Accepted Answer

A) 13.7 rad/s 
B) 7.23 rad/s 
C) 3.70 rad/s 
D) 24.5 rad/s 
E) 16.8 rad/s 
A) 13.7 rad/s 
B) 7.23 rad/s 
C) 3.70 rad/s 
D) 24.5 rad/s 
E) 16.8 rad/s

Question 20

Suppose a uniform solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest.The linear velocity of the sphere at the bottom of the incline depends on

Accepted Answer

A) the mass of the sphere. 
B) the radius of the sphere. 
C) both the mass and the radius of the sphere. 
D) neither the mass nor the radius of the sphere. 
A) the mass of the sphere. 
B) the radius of the sphere. 
C) both the mass and the radius of the sphere. 
D) neither the mass nor the radius of the sphere.

Exam 10: Rotational Kinematics and Energy

A solid uniform cylinder is rolling without slipping.What fraction of its kinetic energy is rotational?

A solid sphere,solid cylinder,and a hollow pipe all have equal masses and radii.If the three of them are released simultaneously at the top of an inclined plane and do not slip,which one will reach the bottom first?

Through how many degrees does a 33 rpm turntable rotate in

A solid sphere and a solid cylinder,both uniform and of the same mass and radius,roll without slipping at the same forward speed.It is correct to say that the total kinetic energy of the solid sphere is

A uniform ball is released from rest on a no-slip surface,as shown in the figure.After reaching its lowest point,the ball begins to rise again,this time on a frictionless surface.When the ball reaches its maximum height on the frictionless surface,it is

A uniform solid disk is released from rest and rolls without slipping down an inclined plane that makes an angle of 25° with the horizontal.What is the forward speed of the disk after it has rolled 3.0 m,measured along the plane?

When a rigid object rotates about a fixed axis,what is true about all the points in the object? (There could be more than one correct choice. )

A solid uniform disk of diameter 3.20 m and mass 42 kg rolls without slipping to the bottom of a hill,starting from rest.If the angular speed of the disk is 4.27 rad/s at the bottom,how high did it start on the hill?

A wheel having a moment of inertia of 5.00 kg ∙ m2 starts from rest and accelerates under a constant torque of 3.00 N ∙ m for 8.00 s.What is the wheel's rotational kinetic energy at the end of 8.00 s?

A solid uniform sphere is rolling without slipping along a horizontal surface with a speed of 5.5 m/s when it starts up a ramp that makes an angle of 25° with the horizontal.What is the speed of the sphere after it has rolled 3.0 m up as measured along the surface of the ramp?

Suppose a solid uniform sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest.The angular velocity of the sphere at the bottom of the incline depends on

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 forward speed of the hoop after it has rolled 3.0 m down as measured along the surface of the ramp?

A wheel rotates through an angle of 13.8 rad as it slows down uniformly from 22.0 rad/s to 13.5 rad/s.What is the magnitude of the angular acceleration of the wheel?

A hoop is rolling without slipping along a horizontal surface with a forward speed of 5.50 m/s when it starts up a ramp that makes an angle of 25.0° with the horizontal.What is the speed of the hoop after it has rolled 3.00 m up as measured along the surface of the ramp?

What is the kinetic energy of a 120-cm thin uniform rod with a mass of 450 g that is rotating about its center at 3.60 rad/s?

A pencil that is 15.7 cm long is released from a vertical position with the eraser end resting on a table.The eraser does not slip as it tips over.Treat the pencil like a uniform rod.What is the angular speed of the pencil just before it hits the table?

Suppose a uniform solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest.The linear velocity of the sphere at the bottom of the incline depends on

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A wheel having a moment of inertia of 5.00 kg ∙ m² starts from rest and accelerates under a constant torque of 3.00 N ∙ m for 8.00 s.What is the wheel's rotational kinetic energy at the end of 8.00 s?