AP Physics C Mechanics 5.3: Torque

Describe torque on a rigid system by combining force magnitude, lever arm, point of application, and direction relative to the rotation axis.

[Maximum number: 6]

A solid uniform disk is supported by a vertical stand. The disk is able to rotate with negligible friction about an axle that passes through the center of the disk. The mass and radius of the disk are given by $M_{\mathrm{d}}$ and R, respectively. The rotational inertia of the disk is $I_{\mathrm{d}}=\frac{1}{2} M_{\mathrm{d}} R^{2}$ . A string of negligible mass is draped over the disk and attached to the top of the disk at point P. One end of the string is connected to an unstretched ideal spring of spring constant k, which is fixed to the ground as shown in Figure 1.
A block of mass $m_{\mathrm{B}}$ is then attached to the string on the right side of the disk. The block is slowly lowered until the spring-disk-block system reaches equilibrium, as shown in Figure 2. In this equilibrium position, the disk has rotated clockwise through a small angle $\theta$ .
Give all algebraic answers in terms of $M_{\mathrm{d}}, R, k, \theta$ , and physical constants, as appropriate.

(a)

At time t=0, the string on the right side of the disk is cut and the block falls to the ground. On the circle below, which represents the disk, draw and label the forces (not components) that act on the disk immediately after the string is cut and the block is falling to the ground. Each force should be represented by an arrow that starts on and is directed away from the point of application.

Figure for Question (a) — AP Physics C: Mechanics

[ 3 ]

For drawing and labeling the force of the tension exerted on the disk anywhere between point P and the left edge of the disk, including point P and the left edge of the disk, tangent to the disk

1 point

For correct location and label of the force due to gravity exerted on the disk, directed straight
down

1 point

For correct location and label of the force exerted on the disk by the axle, directed such that
the disk remains in translational equilibrium (i.e., $\Sigma F=0$ )

1 point

Example Response

Figure for Answer to Question (a) — AP Physics C: Mechanics

Scoring Notes:

- Examples of appropriate labels for the force due to gravity include: $F_{\mathrm{G}}, F_{\mathrm{g}}, F_{\text {grav }}$ , W, m g, M g, "grav force," "F Earth on block," "F on block by Earth," $F_{\text {Earth on block }}$ , $F_{\mathrm{E}, \text { Block }}$ . The labels G and g are not appropriate labels for the force due to gravity. $F_{\mathrm{n}}, F_{\mathrm{N}}, N$ , "normal force," "ground force," or similar labels may be used for the normal force, which can be used instead of $F_{\text {axle }} \cdot F_{\text {spring }}, F_{\mathrm{s}}, T_{\text {spring }}, T$ , "spring force," or similar labels may be used for the tension force exerted by the spring.

- A response with extraneous forces or vectors can earn a maximum of two points.

Total for part (b)

3 points

(b)

The disk is adjusted on the support so that the axle does not pass through the center of mass of the disk. The block is again hung on the right side of the disk and the spring-disk-block system comes to equilibrium, as shown in Figure 3. The axle does not exert a torque on the disk. For each force on the disk, indicate whether the magnitude of the torque about the axle caused by that force increases, decreases, or stays the same relative to part (b).

[ 3 ]

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Covered syllabus points

5.3 Torque question 1

Question (a)

Question (b)