Question 1

Consider an Atwood machine with m2 > m1 and a pulley of mass M. The tension in the string holding mass m2 is

Accepted Answer

A)   larger than the tension in the string holding mass m1.
B)   smaller than the tension in the string holding mass m1.
C)   equal to the tension in the string holding mass m1.
D)   unknown; more information is needed to work out the answer. A

Question 2

A pencil of mass M and length L has a moment of inertia about its center of mass of (1/12) M L2 (assume uniform mass distribution). It balances vertically on the eraser in a state of unstable equilibrium, with a fly of mass m perched on the other end. Assuming the fly hangs on and the eraser does not slip, when M approaches zero, the speed of the fly as it hits the desk is

Accepted Answer

A)   v =  gL\sqrt { g L }gLc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​  /2.
B)   v =  gL\sqrt { g L }gLc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​ 
C)   v =  2gL\sqrt { 2 g L }2gLc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​ 
D)   v = 2  gL\sqrt { g L }gLc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​ 
E)   v = 2  2gL\sqrt { 2 g L }2gLc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​ C

Question 3

A clamp is fastened at the 70-cm mark on a meterstick. Of the two arrangements pictured here, it is easier to balance the system vertically on your hand in

Accepted Answer

A)   the arrangement with the clamp up.
B)   the arrangement with the clamp down.
C)   neither; both arrangements are equally difficult to balance. A

Question 4

The mean orbital speed of Mars is 0.80 times that of the Earth in their orbits around the Sun. Because the mean orbital radius of Mars is 1.52 times that of the Earth, and the mass of Mars is 0.11 times that of the Earth, the ratio of the angular momentum of Mars to that of the Earth in their orbits around the Sun is

Accepted Answer

A)   99.
B)   26.
C)   0.26.
D)   0.21.
E)   0.13.

Question 5

A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/min. When turned off, it rotates 20.0 times at a constant angular acceleration before coming to rest. The angle through which the centrifuge rotates before coming to rest is

Accepted Answer

A)   3.18 rad.
B)   20.0 rad.
C)   80.0 rad.
D)   126 rad.
E)   180 rad.

Question 6

A hoop is rolling (without slipping) on the ground. Its axle travels at 20 m/s with respect to the ground. There are two angular positions on the rim where the instantaneous speed (with respect to the ground) is 20 m/s. The two angular positions are separated by an angle of

Accepted Answer

A)   30o.
B)   60o.
C)   90o.
D)   120o.
E)   180o.

Question 7

A hollow sphere and a solid sphere each made from the same material and having equal maximum radius are rolled from rest (without slipping) the same distance down an inclined plane. The travel time of the hollow sphere is

Accepted Answer

A)   smaller than the travel time of the solid sphere.
B)   larger than the travel time of the solid sphere.
C)   the same as the travel time of the solid sphere.
D)   unknown; more information is needed to work out the answer.

Question 8

Large meteors can strike the Earth with speeds of $80,000 \mathrm {~km} / \mathrm { h }$. Such a meteor hits the Earth (radius $6.37 \times 10 ^ { 6 } \mathrm {~m}$ ) at a point on the plane of the Earth's equator at $80,000 \mathrm {~km} / \mathrm { h }$, resulting in a change of the Earth's angular momentum of $80.0 \times 10 ^ { 12 } \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$. The meteor's mass is

Accepted Answer

A)   13.0 kg.
B)   56.0 kg.
C)   126 kg.
D)   565 kg.
E)   637 kg.

Question 9

A boy stands at the center of a merry-go-round platform that rotates at constant angular velocity. When the boy starts walking radially toward the edge, the platform's angular velocity

Accepted Answer

A)   increases.
B)   does not change.
C)   decreases.
D)   becomes zero.

Question 10

A potter's wheel (assuming a uniform disk of mass 5.0 kg and diameter 0.50 m) rotates around a vertical axis through its center at a frequency of 10 rad/s. The potter throws a 4.0-kg chunk of clay, shaped as a flat disk of radius 6.0 cm, onto the center of the rotating wheel. The frequency of rotation of the wheel after the clay sticks to it is

Accepted Answer

A)   8.4 rad/s.
B)   9.6 rad/s.
C)   10 rad/s.
D)   12 rad/s.
E)   19 rad/s.

Question 11

A bicycle of mass 25 kg has wheels of mass 5.0 kg and radii of 30 cm each (assume the wheels are uniform disks). The part of the kinetic energy that is rotational is

Accepted Answer

A)   10%.
B)   17%.
C)   20%.
D)   34%.
E)   40%.

Question 12

A wheel is rolling (without slipping) on the ground. Its axle travels at 30 m/s with respect to the ground. The instantaneous speed (with respect to the ground) of a point on the rim directly above the axle is

Accepted Answer

A)   15 m/s.
B)   30 m/s.
C)   45 m/s.
D)   60 m/s.
E)   90 m/s.

Question 13

A top is spinning rapidly on a table, its axis inclined to the vertical. As the spin of the top gradually decreases, the precession frequency of the top

Accepted Answer

A)   increases.
B)   decreases.
C)   remains unchanged.
D)   is unknown; more information is needed to work out the answer.

Question 14

You are trying to open a door that is stuck by pulling on the doorknob in a direction perpendicular to the door. If you instead tie a rope to the doorknob and then pull with the same force, the torque you exert on the door

Accepted Answer

A)   increases.
B)   stays the same.
C)   decreases.
D)   is zero.

Question 15

Some old-fashioned bicycles had a front wheel with a large diameter compared to the diameter of the back wheel. When rolling without slipping on a horizontal surface, the two wheels were subject to the same

Accepted Answer

A)   linear velocity at the rim.
B)   angular velocity.
C)   angular acceleration.
D)   tangential acceleration at the rim.
E)   centripetal acceleration at the rim.

Question 16

A wheel of radius R is rolling without slipping on a horizontal surface. The frictional force exerted by the surface on the wheel at the point where the rim is in contact with the surface is

Accepted Answer

A)   tangent to the surface, pointing in the same direction as the velocity of the center of mass.
B)   tangent to the surface, pointing in the direction opposite that of the velocity of the center of mass.
C)   zero.
D)   normal to the surface, pointing toward the wheel's center of mass.
E)   normal to the surface, pointing away from the wheel's center of mass.

Question 17

A disk of moment of inertia 80 kg.m2 is free to rotate about its axis (through the center, perpendicular to the plane of the disk, which is set vertical). To increase its angular velocity uniformly from rest to 5.0 rad/s in 20.0 s, the work done by the applied torque is

Accepted Answer

A)   1.0 * 103 J.
B)   4.0 F*102 J.
C)   2.0 * 102 J.
D)   3.2 J.
E)   1.6 J.

Question 18

The protons and neutrons making up a nucleus are suddenly rearranging themselves so that the nucleus' moment of inertia decreases by a factor of 4. The change in the rotational kinetic energy during this process is

Accepted Answer

A)   zero.
B)   2 times the initial kinetic energy of rotation.
C)   3 times the initial kinetic energy of rotation.
D)   4 times the initial kinetic energy of rotation.
E)   16 times the initial kinetic energy of rotation.

Question 19

A boy stands on a merry-go-round platform at rest. When the boy starts walking tangentially along the edge of the platform in a clockwise direction, the platform will

Accepted Answer

A)   start rotating in a clockwise direction.
B)   stay at rest until an external force acts on it.
C)   stay at rest until an external torque acts on it.
D)   start rotating in a counterclockwise direction.

Question 20

A baseball player increases the speed of a bat from rest to 20.0 rad/s in 0.25 s at a constant acceleration. Assuming the bat is a 2.0-kg rod of uniform mass distribution and of length 1.0 m, the torque applied by the player to one end of the bat is

Accepted Answer

A)   10 N.m.
B)   13 N.m.
C)   40 N.m.
D)   53 N.m.
E)   1.6*102 N.m.

Exam 13: Dynamics of a Rigid Body

Consider an Atwood machine with m₂> m₁and a pulley of mass M. The tension in the string holding mass m₂ is

A clamp is fastened at the 70-cm mark on a meterstick. Of the two arrangements pictured here, it is easier to balance the system vertically on your hand in

A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/min. When turned off, it rotates 20.0 times at a constant angular acceleration before coming to rest. The angle through which the centrifuge rotates before coming to rest is

A hoop is rolling (without slipping) on the ground. Its axle travels at 20 m/s with respect to the ground. There are two angular positions on the rim where the instantaneous speed (with respect to the ground) is 20 m/s. The two angular positions are separated by an angle of

A hollow sphere and a solid sphere each made from the same material and having equal maximum radius are rolled from rest (without slipping) the same distance down an inclined plane. The travel time of the hollow sphere is

A boy stands at the center of a merry-go-round platform that rotates at constant angular velocity. When the boy starts walking radially toward the edge, the platform's angular velocity

A bicycle of mass 25 kg has wheels of mass 5.0 kg and radii of 30 cm each (assume the wheels are uniform disks) . The part of the kinetic energy that is rotational is

A wheel is rolling (without slipping) on the ground. Its axle travels at 30 m/s with respect to the ground. The instantaneous speed (with respect to the ground) of a point on the rim directly above the axle is

A top is spinning rapidly on a table, its axis inclined to the vertical. As the spin of the top gradually decreases, the precession frequency of the top

You are trying to open a door that is stuck by pulling on the doorknob in a direction perpendicular to the door. If you instead tie a rope to the doorknob and then pull with the same force, the torque you exert on the door

Some old-fashioned bicycles had a front wheel with a large diameter compared to the diameter of the back wheel. When rolling without slipping on a horizontal surface, the two wheels were subject to the same

A wheel of radius R is rolling without slipping on a horizontal surface. The frictional force exerted by the surface on the wheel at the point where the rim is in contact with the surface is

A disk of moment of inertia 80 kg.m² is free to rotate about its axis (through the center, perpendicular to the plane of the disk, which is set vertical) . To increase its angular velocity uniformly from rest to 5.0 rad/s in 20.0 s, the work done by the applied torque is

The protons and neutrons making up a nucleus are suddenly rearranging themselves so that the nucleus' moment of inertia decreases by a factor of 4. The change in the rotational kinetic energy during this process is

A boy stands on a merry-go-round platform at rest. When the boy starts walking tangentially along the edge of the platform in a clockwise direction, the platform will

A baseball player increases the speed of a bat from rest to 20.0 rad/s in 0.25 s at a constant acceleration. Assuming the bat is a 2.0-kg rod of uniform mass distribution and of length 1.0 m, the torque applied by the player to one end of the bat is

Exam 13: Dynamics of a Rigid Body

Consider an Atwood machine with m2 > m1 and a pulley of mass M. The tension in the string holding mass m2 is

A clamp is fastened at the 70-cm mark on a meterstick. Of the two arrangements pictured here, it is easier to balance the system vertically on your hand in

A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/min. When turned off, it rotates 20.0 times at a constant angular acceleration before coming to rest. The angle through which the centrifuge rotates before coming to rest is

A hoop is rolling (without slipping) on the ground. Its axle travels at 20 m/s with respect to the ground. There are two angular positions on the rim where the instantaneous speed (with respect to the ground) is 20 m/s. The two angular positions are separated by an angle of

A hollow sphere and a solid sphere each made from the same material and having equal maximum radius are rolled from rest (without slipping) the same distance down an inclined plane. The travel time of the hollow sphere is

A boy stands at the center of a merry-go-round platform that rotates at constant angular velocity. When the boy starts walking radially toward the edge, the platform's angular velocity

A bicycle of mass 25 kg has wheels of mass 5.0 kg and radii of 30 cm each (assume the wheels are uniform disks) . The part of the kinetic energy that is rotational is

A wheel is rolling (without slipping) on the ground. Its axle travels at 30 m/s with respect to the ground. The instantaneous speed (with respect to the ground) of a point on the rim directly above the axle is

A top is spinning rapidly on a table, its axis inclined to the vertical. As the spin of the top gradually decreases, the precession frequency of the top

You are trying to open a door that is stuck by pulling on the doorknob in a direction perpendicular to the door. If you instead tie a rope to the doorknob and then pull with the same force, the torque you exert on the door

Some old-fashioned bicycles had a front wheel with a large diameter compared to the diameter of the back wheel. When rolling without slipping on a horizontal surface, the two wheels were subject to the same

A wheel of radius R is rolling without slipping on a horizontal surface. The frictional force exerted by the surface on the wheel at the point where the rim is in contact with the surface is

A disk of moment of inertia 80 kg.m2 is free to rotate about its axis (through the center, perpendicular to the plane of the disk, which is set vertical) . To increase its angular velocity uniformly from rest to 5.0 rad/s in 20.0 s, the work done by the applied torque is

The protons and neutrons making up a nucleus are suddenly rearranging themselves so that the nucleus' moment of inertia decreases by a factor of 4. The change in the rotational kinetic energy during this process is

A boy stands on a merry-go-round platform at rest. When the boy starts walking tangentially along the edge of the platform in a clockwise direction, the platform will

A baseball player increases the speed of a bat from rest to 20.0 rad/s in 0.25 s at a constant acceleration. Assuming the bat is a 2.0-kg rod of uniform mass distribution and of length 1.0 m, the torque applied by the player to one end of the bat is

Consider an Atwood machine with m₂> m₁and a pulley of mass M. The tension in the string holding mass m₂ is

A disk of moment of inertia 80 kg.m² is free to rotate about its axis (through the center, perpendicular to the plane of the disk, which is set vertical) . To increase its angular velocity uniformly from rest to 5.0 rad/s in 20.0 s, the work done by the applied torque is