AP Rotation review

The diagram shows two wheels of radius r and 3r connected to each other and mounted on frictionless bearings. A mass m₁ hangs from a string wrapped around the smaller wheel while a mass m₂ hangs from a string wrapped around the larger wheel. If the system remains at rest even after being released, which of the following must be true?

• m₁ = 3m₂

• m₁ = 9m₂

• m₂ = 3m₁

• m₂ = 9m₁

The diagram shows two wheels of radius r and 3r connected to each other and mounted on frictionless bearings. A mass m₁ hangs from a string wrapped around the smaller wheel while a mass m₂ hangs from a string wrapped around the larger wheel. Suppose both masses are equal. If the system is released from rest, which mass will accelerate upward?

• m₁

• m₂

Three forces of equal magnitude are incident on a regular hexagon that is initially at rest and not rotating. How will the hexagon rotate as a result of the action of these three forces?

• clockwise

• counterclockwise

• it will not rotate

Three forces of equal magnitude are incident on a regular hexagon that is initially at rest and not rotating. In what direction will the hexagon’s center of mass accelerate as a result of the action of these three forces?

• right

• left

• up

• down

A plank of total length L is set on the flat roof of a building so that the length of the plank that is over the edge of the building is x. A person who has the same mass as the plank will walk out onto the plank all the way to the end. What is the maximum value that x can have if the plank is not to tip at any time while the person walks out towards its end?

• L/6

• L/4

• L/3

• L/2

The figure shows a system which consists of a disk of mass 3m supported on frictionless bearings by a stand that has a mass of 4m. Blocks m and 2m hang from opposite ends of a string that passes over the disk. The system is released from rest. Which of the following statements are true of the system after it is released? Select two answers.

• The tensions are equal to each other.

• The torques are equal to each other.

• The magnitudes of the accelerations of m and 2m are equal.

• The torque causing the pulley to rotate is equal to r (T₂-T₁)