Torque (College Board AP® Physics 1: Algebra-Based): Exam Questions

Figure 1

A block of unknown mass is attached to a long, lightweight string that is wrapped several turns around a pulley mounted on a horizontal axis through its center, as shown in Figure 1. The pulley is a uniform solid disk of mass and radius . The pulley can rotate about its center with negligible friction. The string does not slip on the pulley as the block falls.

When the block is released from rest and as the block travels toward the ground, the magnitude of the tension exerted on the block by the string is .

The circle in Figure 2 represents the pulley. On Figure 2, draw and label the forces (not components) exerted on the pulley after the block is released. Draw each force as a distinct arrow starting on, and pointing away from, the point at which the force is exerted.

Figure 2

Figure 3

Scenarios 1 and 2 show two different pulleys. In Scenario 1, the pulley is a uniform solid disk of mass and radius . In Scenario 2, the pulley is a hoop that has the same mass and radius as the disk. Each pulley has a lightweight string wrapped around it several turns and is mounted on a horizontal axle, as shown in Figure 3. Each pulley is free to rotate about its center with negligible friction. In both scenarios, the pulleys begin at rest. Then both strings are pulled with the same constant force for the same time interval , causing the pulleys to rotate without the string slipping.

Indicate whether the torque exerted on the hoop is greater than, equal to, or less than the torque exerted on the disk. Justify your reasoning.

Figure 1

A rod with a sphere attached to the end is connected to a horizontal mounted axle and carefully balanced so that it rests in a position vertically upward from the axle. The center of mass of the rod-sphere system is indicated with a , as shown in Figure 1. The sphere is lightly tapped, and the rod-sphere system rotates clockwise with negligible friction about the axle due to the gravitational force.

A student takes a video of the rod rotating from the vertically upward position to the vertically downward position. Figure 2 shows five frames (still shots) that the student selected from the video.

Note: these frames are not equally spaced apart in time.

Figure 2

In which of the frames of the video in Figure 2 is the magnitude of the torque exerted on the rod-sphere system the greatest? Justify your answer without deriving or manipulating equations.

Figure 3

The rod-sphere system has mass and length , and the center of mass of the rod-sphere system is located a distance from the axle, as shown in Figure 3.

Determine an expression for the maximum torque exerted on the rod-sphere system from the moment shown in Frame A to the moment shown in Frame E. Express your answer in terms of , , and fundamental constants, as appropriate.

Figure 1

Two pulleys with different radii are attached to each other so that they rotate together about a horizontal axle through their common center. There is negligible friction in the axle. Object 1 has mass and hangs from a light string wrapped around the larger pulley of radius , while Object 2 has mass and hangs from another light string wrapped around the smaller pulley of radius , as shown in Figure 1. At time , the pulleys are released from rest and the objects begin to accelerate.

The following circles represent the pulleys in Figure 1. On the circles, draw and label arrows that represent the forces (not components) that are exerted on the pulleys after they are released. Draw each force as a distinct arrow starting on and pointing away from the point at which the force is exerted. The lengths of the arrows should reflect the relative magnitudes of the forces exerted at each point.

Determine an expression for the magnitude of the net torque exerted on the objects-pulleys system about the axle after the pulleys are released in terms of , , and physical constants as appropriate.

A student makes the following claim:

"The expression for the net torque exerted on the objects-pulleys system must include the tension forces in the strings."

Indicate whether or not the student's claim is correct. Justify your answer.

Figure 1

A nonuniform bar is attached to a wall by a fixed pivot at its left end, as shown in Figure 1. The bar has length and mass . Its mass is distributed such that the bar's center of mass is a distance from the bar's free end and the bar's rotational inertia about the pivot is . A string attached to the wall and to the bar keeps it horizontal.

The bar from Figure 1 is shown in Figure 2. The dots in Figure 2 represent the point of attachment of the string and the bar's center of mass.

On Figure 2, draw and label the forces (not components) exerted on the bar. Each force must be represented by a distinct arrow starting on, and pointing away from, the point at which the force is exerted on the bar.

Figure 2

Figure 3

A different string is then attached to the bar so that it is lined up with the bar's center of mass, as shown in Figure 3. The string is also attached to a higher location on the wall so that it is oriented at the same angle as the original string and keeps the bar horizontal.

Other than the force exerted by the string, indicate how a force represented in the diagram you drew for part a) would change, if at all, with the second string attached to the bar and wall as in Figure 3. Justify your answer.