Torque and Angular Momentum and Kinetic Energy

Two forces produce equal torques on a door about the door hinge.  The first force is applied at the midpoint of the door; the second force is applied at the doorknob.  Both forces are applied perpendicular to the door.  Which force has a greater magnitude?

• the second force (at the doorknob)
• The two forces are equal.
• the first force (at the midpoint)

As shown in the figure, a given force is applied to a rod in several different ways. In which case is the torque about the pivot P due to this force the greatest?

• 1
• 2
• 3
• 4

Five forces act on a rod that is free to pivot at point P, as shown in the figure. Which of these forces is producing a counter-clockwise torque about point P? 

• force E
• force B
• force C
• force D

A person sits on a freely spinning lab stool that has no friction in its axle. When this person extends her arms,

• her moment of inertia increases and her angular speed decreases.
• her moment of inertia decreases and her angular speed increases.
• her moment of inertia increases and her angular speed increases.
• her moment of inertia increases and her angular speed remains the same.

A merry-go-round spins freely when Diego moves quickly to the center along a radius of the merry-go-round. As he does this, it is true to say that

• the moment of inertia of the system increases and the angular speed increases.
• the moment of inertia of the system decreases and the angular speed remains the same.
• the moment of inertia of the system decreases and the angular speed decreases.
• the moment of inertia of the system decreases and the angular speed increases.

A uniform solid cylinder with a radius of 10 cm and a mass of 3.0 kg is rotating about its center with an angular speed of 33.4 rpm. What is its kinetic energy?

• 0.092 J
• 17 J
• 1.1 J
• 0.18 J

The lug nuts on a car wheel require tightening to a torque of 90 N ∙ m.  If a 30-cm long wrench is used, what is the magnitude of the minimum force required using the wrench?

• 30 N
• 150N
• 15 N
• 300 N

A man in a gym is holding an 8.0-kg weight at arm's length, a distance of 0.55 m from his shoulder joint. What is the torque about his shoulder joint due to the weight if his arm is horizontal?

• 43 N ∙ m
• 0 N ∙ m
• 15 N ∙ m
• 0.24 N ∙ m

The drive chain in a bicycle is applying a torque of 0.850 N ∙ m to the wheel of the bicycle. You can treat the wheel as a thin uniform hoop (or ring) with a mass of 0.750 kg and a radius of 33.0 cm. What is the angular acceleration of the wheel?

• 10.4 rad/s2
• 3.43 rad/s2
• 5.20 rad/s2
• 1.06 rad/s2

A force of 16.88 N is applied tangentially to a wheel of radius 0.340 m and causes an angular acceleration of 1.20 rad/s2. What is the moment of inertia of the wheel?

• 3.59 kg ∙ m2
• 5.59 kg ∙ m2
• 4.78 kg ∙ m2
• 7.17 kg ∙ m2