Question 1

Two wheels roll side-by-side without sliding, at the same speed.The radius of wheel 2 is twice the radius of wheel 1.The angular velocity of wheel 2 is:

Accepted Answer

A) twice the angular velocity of wheel 1 
B) the same as the angular velocity of wheel 1 
C) half the angular velocity of wheel 1 
D) more than twice the angular velocity of wheel 1 
E) less than half the angular velocity of wheel 1 
A) twice the angular velocity of wheel 1 
B) the same as the angular velocity of wheel 1 
C) half the angular velocity of wheel 1 
D) more than twice the angular velocity of wheel 1 
E) less than half the angular velocity of wheel 1

Question 2

The unit kg.m2/s can be used for:

Accepted Answer

A) angular momentum 
B) rotational kinetic energy 
C) rotational inertia 
D) torque 
E) power 
A) angular momentum 
B) rotational kinetic energy 
C) rotational inertia 
D) torque 
E) power

Question 3

Two objects are moving in the x, y plane as shown.If a net torque of 44 N∙m acts on them for 5.0 seconds, what is the change in their angular momentum?

Accepted Answer

A) 0 kg∙m2/s 
B) 6 kg∙m2/s 
C) 30 kg∙m2/s 
D) 150 kg∙m2/s 
E) 220 kg∙m2/s 
A) 0 kg∙m2/s 
B) 6 kg∙m2/s 
C) 30 kg∙m2/s 
D) 150 kg∙m2/s 
E) 220 kg∙m2/s

Question 4

A uniform disk, a thin hoop, and a uniform sphere, all with the same mass and same outer radius, are each free to rotate about a fixed axis through its center.Assume the hoop is connected to the rotation axis by light spokes.With the objects starting from rest, identical forces are simultaneously applied to the rims, as shown.Rank the objects according to their angular momenta after a given time t, least to greatest.

Accepted Answer

A) all tie 
B) disk, hoop, sphere 
C) sphere, disk, hoop 
D) hoop, sphere, disk 
E) hoop, disk, sphere 
A) all tie 
B) disk, hoop, sphere 
C) sphere, disk, hoop 
D) hoop, sphere, disk 
E) hoop, disk, sphere

Question 5

A wheel rolls without slipping along a horizontal road as shown.The velocity of the center of the wheel is represented by   .Point P is painted on the rim of the wheel.The direction of the instantaneous velocity of point P is:

Accepted Answer

A) $\rightarrow$ 
B) $\leftarrow$ 
C) $\uparrow$ 
D)  " " 
E) "zero" 
A) $\rightarrow$ 
B) $\leftarrow$ 
C) $\uparrow$ 
D)  " " 
E) "zero"

Question 6

A yo-yo, arranged as shown, rests on a frictionless surface.When a force   is applied to the string as shown, the yo-yo:

Accepted Answer

A) moves to the left and rotates counterclockwise 
B) moves to the right and rotates counterclockwise 
C) moves to the left and rotates clockwise 
D) moves to the right and rotates clockwise 
E) moves to the right and does not rotate 
A) moves to the left and rotates counterclockwise 
B) moves to the right and rotates counterclockwise 
C) moves to the left and rotates clockwise 
D) moves to the right and rotates clockwise 
E) moves to the right and does not rotate

Question 7

A 15-g paper clip is attached to the rim of a phonograph record with a diameter of 30 cm, spinning at 3.5 rad/s.The magnitude of its angular momentum is:

Accepted Answer

A) 1.2   x  10-3 kg.m2/s 
B) 4.7   x  10-3 kg.m2/s 
C) 7.9   x  10-3 kg.m2/s 
D) 1.6   x  10-2 kg.m2/s 
E) 1.2 kg.m2/s 
A) 1.2   x  10-3 kg.m2/s 
B) 4.7   x  10-3 kg.m2/s 
C) 7.9   x  10-3 kg.m2/s 
D) 1.6   x  10-2 kg.m2/s 
E) 1.2 kg.m2/s

Question 8

A hoop rolls with constant velocity and without sliding along level ground.Its rotational kinetic energy is:

Accepted Answer

A) half its translational kinetic energy 
B) the same as its translational kinetic energy 
C) twice its translational kinetic energy 
D) four times its translational kinetic energy 
E) one-third its translational kinetic energy 
A) half its translational kinetic energy 
B) the same as its translational kinetic energy 
C) twice its translational kinetic energy 
D) four times its translational kinetic energy 
E) one-third its translational kinetic energy

Question 9

Two uniform cylinders have different masses and different rotational inertias.They simultaneously start from rest at the top of an inclined plane and roll without sliding down the plane.The cylinder that gets to the bottom first is:

Accepted Answer

A) the one with the larger mass 
B) the one with the smaller mass 
C) the one with the larger rotational inertia 
D) the one with the smaller rotational inertia 
E) neither (they arrive together) 
A) the one with the larger mass 
B) the one with the smaller mass 
C) the one with the larger rotational inertia 
D) the one with the smaller rotational inertia 
E) neither (they arrive together)

Question 10

Which of the following is a vector quantity?

Accepted Answer

A) angular speed 
B) rotational inertia 
C) rotational kinetic energy 
D) mass 
E) torque 
A) angular speed 
B) rotational inertia 
C) rotational kinetic energy 
D) mass 
E) torque

Question 11

A uniform sphere of radius R rotates about a diameter with angular momentum of magnitude L.Under the action of internal forces the sphere collapses to a uniform sphere of radius R/2.The magnitude of its new angular momentum is:

Accepted Answer

A) L/4 
B) L/2 
C) L 
D) 2L 
E) 4L 
A) L/4 
B) L/2 
C) L 
D) 2L 
E) 4L

Question 12

A hoop, a uniform disk, and a uniform sphere, all with the same mass and outer radius, start with the same speed and roll without sliding up identical inclines.Rank the objects according to how high they go, least to greatest.

Accepted Answer

A) hoop, disk, sphere 
B) disk, hoop, sphere 
C) sphere, hoop, disk 
D) sphere, disk, hoop 
E) hoop, sphere, disk 
A) hoop, disk, sphere 
B) disk, hoop, sphere 
C) sphere, hoop, disk 
D) sphere, disk, hoop 
E) hoop, sphere, disk

Question 13

An ice skater with rotational inertia I0 is spinning with angular speed    0.She pulls her arms in, thereby increasing her angular speed to 4   0.Her rotational inertia is then:

Accepted Answer

A) I0 
B) I0 /2 
C) 2 I0 
D) I0 /4 
E) 4 I0 
A) I0 
B) I0 /2 
C) 2 I0 
D) I0 /4 
E) 4 I0

Question 14

A particle, held by a string whose other end is attached to a fixed point C, moves in a circle on a horizontal frictionless surface.If the string is cut, the angular momentum of the particle about the point C:

Accepted Answer

A) increases 
B) decreases 
C) does not change 
D) changes direction but not magnitude 
E) none of these 
A) increases 
B) decreases 
C) does not change 
D) changes direction but not magnitude 
E) none of these

Question 15

A forward force acting on the axle accelerates a rolling wheel on a horizontal surface.If the wheel does not slide the frictional force of the surface on the wheel is:

Accepted Answer

A) zero 
B) in the forward direction and does zero work on the wheel 
C) in the forward direction and does positive work on the wheel 
D) in the backward direction and does zero work on the wheel 
E) in the backward direction and does positive work on the wheel 
A) zero 
B) in the forward direction and does zero work on the wheel 
C) in the forward direction and does positive work on the wheel 
D) in the backward direction and does zero work on the wheel 
E) in the backward direction and does positive work on the wheel

Question 16

A force   = 4.2 N   + 3.7 N   + 1.2 N   acts on a particle located at x = 3.3 m.What is the torque on the particle around the origin?

Accepted Answer

A) 14 N∙m   
B) -4.0 N∙m   + 12 N∙m
  
C) 12 N∙m   
D) 14 N∙m   - 4.0 N∙m
  + 12 N∙m
  
E) cannot be calculated without knowing the mass of the particle 
A) 14 N∙m   
B) -4.0 N∙m   + 12 N∙m
  
C) 12 N∙m   
D) 14 N∙m   - 4.0 N∙m
  + 12 N∙m
  
E) cannot be calculated without knowing the mass of the particle

Question 17

A uniform disk has radius R and mass M.When it is spinning with angular velocity    about an axis through its center and perpendicular to its face its angular momentum is I   .When it is spinning with the same angle velocity about a parallel axis a distance h away its angular momentum is:

Accepted Answer

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

Question 18

Two identical disks, with rotational inertia I (= 1/2 MR2), roll without slipping across a horizontal floor and then up inclines.Disk A rolls up its incline without sliding.On the other hand, disk B rolls up a frictionless incline.Otherwise the inclines are identical.Disk A reaches a height 12 cm above the floor before rolling down again.Disk B reaches a height above the floor of:

Accepted Answer

A) 24 cm 
B) 18 cm 
C) 12 cm 
D) 8 cm 
E) 6 cm 
A) 24 cm 
B) 18 cm 
C) 12 cm 
D) 8 cm 
E) 6 cm

Question 19

What is precession?

Accepted Answer

A) Precession is the action of a solid rolling up a slope, prior to rolling back down again. 
B) Precession is the increase in economic activity before a recession. 
C) Precession is the rotation of a solid around a fixed axis. 
D) Precession is the rotation of an angular momentum vector around a vertical axis. 
E) Precession is the oscillatory motion of an angular momentum vector as it rotates around a vertical axis. 
A) Precession is the action of a solid rolling up a slope, prior to rolling back down again. 
B) Precession is the increase in economic activity before a recession. 
C) Precession is the rotation of a solid around a fixed axis. 
D) Precession is the rotation of an angular momentum vector around a vertical axis. 
E) Precession is the oscillatory motion of an angular momentum vector as it rotates around a vertical axis.

Question 20

A 2.0-kg stone is tied to a 0.50 m long string and swung around a circle at a constant angular velocity of 12 rad/s.The circle is parallel to the xy plane and is centered on the z axis, 0.75 m from the origin.The magnitude of the torque about the origin is:

Accepted Answer

A) 0 N∙m 
B) 6.0 N∙m 
C) 14 N∙m 
D) 72 N∙m 
E) 108 N∙m 
A) 0 N∙m 
B) 6.0 N∙m 
C) 14 N∙m 
D) 72 N∙m 
E) 108 N∙m

Exam 11: Rolling, Torque, and Angular Momentum

Two wheels roll side-by-side without sliding, at the same speed.The radius of wheel 2 is twice the radius of wheel 1.The angular velocity of wheel 2 is:

The unit kg.m2/s can be used for:

Two objects are moving in the x, y plane as shown.If a net torque of 44 N∙m acts on them for 5.0 seconds, what is the change in their angular momentum?

A wheel rolls without slipping along a horizontal road as shown.The velocity of the center of the wheel is represented by .Point P is painted on the rim of the wheel.The direction of the instantaneous velocity of point P is:

A yo-yo, arranged as shown, rests on a frictionless surface.When a force is applied to the string as shown, the yo-yo:

A 15-g paper clip is attached to the rim of a phonograph record with a diameter of 30 cm, spinning at 3.5 rad/s.The magnitude of its angular momentum is:

A hoop rolls with constant velocity and without sliding along level ground.Its rotational kinetic energy is:

Two uniform cylinders have different masses and different rotational inertias.They simultaneously start from rest at the top of an inclined plane and roll without sliding down the plane.The cylinder that gets to the bottom first is:

Which of the following is a vector quantity?

A uniform sphere of radius R rotates about a diameter with angular momentum of magnitude L.Under the action of internal forces the sphere collapses to a uniform sphere of radius R/2.The magnitude of its new angular momentum is:

A hoop, a uniform disk, and a uniform sphere, all with the same mass and outer radius, start with the same speed and roll without sliding up identical inclines.Rank the objects according to how high they go, least to greatest.

An ice skater with rotational inertia I0 is spinning with angular speed 0.She pulls her arms in, thereby increasing her angular speed to 4 0.Her rotational inertia is then:

A particle, held by a string whose other end is attached to a fixed point C, moves in a circle on a horizontal frictionless surface.If the string is cut, the angular momentum of the particle about the point C:

A forward force acting on the axle accelerates a rolling wheel on a horizontal surface.If the wheel does not slide the frictional force of the surface on the wheel is:

A force = 4.2 N + 3.7 N + 1.2 N acts on a particle located at x = 3.3 m.What is the torque on the particle around the origin?

A uniform disk has radius R and mass M.When it is spinning with angular velocity about an axis through its center and perpendicular to its face its angular momentum is I .When it is spinning with the same angle velocity about a parallel axis a distance h away its angular momentum is:

What is precession?

A 2.0-kg stone is tied to a 0.50 m long string and swung around a circle at a constant angular velocity of 12 rad/s.The circle is parallel to the xy plane and is centered on the z axis, 0.75 m from the origin.The magnitude of the torque about the origin is:

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The unit kg.m²/s can be used for:

An ice skater with rotational inertia I₀ is spinning with angular speed ₀.She pulls her arms in, thereby increasing her angular speed to 4 ₀.Her rotational inertia is then: