AP REVIEW Rotation

The figure above shows a uniform meterstick

that is set on a fulcrum at its center. A force of

magnitude F toward the bottom of the page is

exerted on the meterstick at the position shown.

At which of the labeled positions must an upward

force of magnitude 2F be exerted on the

meterstick to keep the meterstick in equilibrium?

• A

• B

• C

• D

Two satellites are in circular orbits around Earth.

Satellite A has speed Av . Satellite B has an

orbital radius nine times that of satellite A.

What is the speed of satellite B ?

• $\frac{v_a}{9}$

• $\frac{v_a}{3}$

• $3v_a$

• $9v_a$

A solid metal bar is at rest on a horizontal frictionless surface. It is free to rotate about a vertical axis at the left end. The figures below show forces of different magnitudes that are exerted on the bar at different locations. In which

case does the bar’s angular speed about the axis increase at the fastest rate?

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TWO ANSWERS

A ball attached to a light string swings in a counterclockwise vertical circle, as shown above. Which of the following arrows represent one of the forces exerted on the ball at the moment it passes through point P ? Select two answers.

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TWO ANSWERS

Some bicycle brakes work by pressing rubber pads against the rim of the wheel. To test newly designed brakes, bicycle engineers mount a wheel of known rotational inertia on a low-friction axle, as shown above. The engineers spin the wheel with known initial angular speed and then apply

the brakes with a constant force. Which of the following procedures would enable the engineers to find the torque exerted by the brakes on the wheel? Select two answers.

• Measuring how much time the wheel takes to come to rest

• Measuring how many rotations the wheel completes while coming to rest

• Measuring the distance from axle to brakes and the normal force between the rubber pads and the rim

• Measuring the mechanical energy dissipated as the rim rubs against the rubber pads.

A system consists of a disk rotating on a frictionless axle and a piece of clay moving toward it, as shown in the figure above. The outside edge of the disk is moving at a linear

speed v, and the clay is moving at speed v 2 . The clay sticks to the outside edge of the disk. How does the angular momentum of the system after the clay sticks compare to the angular momentum of the system before the clay sticks, and what is an explanation for the comparison?

• It is the same because there is no external torque acting on the system.

• It is greater because the rotating mass increases, which increases the rotational inertia.

• It is less because the speed of the disk decreases when the clay sticks to it.

• It is less because the angular momentum of the clay opposes that of the disk

A disk of known radius and rotational inertia can rotate without friction in a horizontal plane around its fixed central axis. The disk has a cord of negligible mass wrapped around its edge. The disk is initially at rest, and the cord can be pulled to make the disk rotate. Which of the following procedures would best determine the relationship between applied torque and the resulting change

in angular momentum of the disk?

• Pulling on the cord, exerting a force of 15 N for 2 s and then 25 N for 3 s, and measuring the final angular velocity of the disk

• For five different time intervals, pulling on the cord, exerting a force of 15 N, and then measuring the angle through which the disk rotates in each case

• For five different time intervals, pulling on the cord, exerting a force of 15 N, and then measuring the final angular velocity

  of the disk

• For five forces of different magnitude, pulling on the cord for 5 s, and then measuring the final angular velocity of the disk