AP Physics 1: Algebra-Based 5.3 Torque Questions

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

Exam points

use force lines of action and lever arms to identify zero and nonzero torques about an axis
draw force diagrams that preserve each force's direction and point of application
calculate individual torques and sum signed contributions for beams, disks and pulley systems
rank rotational effects as force magnitude, angle or distance from the pivot changes
solve for force magnitudes or combinations that produce zero net torque about a pivot

Covered syllabus points

5.3.A—Identify the torques exerted on a rigid system 5.3.B—Describe the torques exerted on a rigid system

[Maximum number: 1]

Figure for Question 1 — AP Physics 1: Algebra-Based

8 points; suggested time: 15-20 minutes A mass m is initially resting at the center of a rotating disk with rotational inertia $(1 / 2) M R^{2}$ . The entire system is freely rotating with an initial angular speed of $w_{0}$ . As time goes by, the mass is carefully moved at a constant speed outward from the center. This is done in such a way that no torque on the system is introduced.

How can one push the small mass m such that no torque is induced?

[Maximum number: 3]

(12 points, suggested time 25 minutes)
The left end of a uniform beam of mass M and length L is attached to a wall by a hinge, as shown in Figure 1. One end of a string with negligible mass is attached to the right end of the beam. The other end of the string is attached to the wall above the hinge at Point 1. The beam remains horizontal. The hinge exerts a force on the beam of magnitude $F_{\mathrm{H}}$ , and the angle between the beam and the string is $\theta=\theta_{1}$ .

The following rectangle represents the beam in Figure 1. On the rectangle, draw and label the forces (not components) exerted on the beam. Draw each force as a distinct arrow starting on, and pointing away from, the point at which the force is exerted.

Figure 2

For drawing the gravitational force at the center of the beam that is directed downward For drawing the tension force at the right end of the beam that is directed upward and leftward

For a diagram with three force vectors that represent a system in equilibrium

Example Response

Figure for Answer to Question 2 — AP Physics 1: Algebra-Based

Scoring Note: Examples of appropriate labels for the gravitational force include $F_{G}, F_{g}$ , $F_{\text {grav }}, W, m g, M g$ , "grav force," F Earth on beam," " F on beam by Earth," $F_{\text {Earth on Beam }}, F_{\mathrm{E}, \text { Beam }}$ , or $F_{\text {Beam }, \mathrm{E}}$ . The labels G or g are not appropriate labels for the gravitational force.

Scoring Note: Examples of appropriate labels for the normal force include $F_{n}, F_{N}, N$ , "normal force," or "wall force."

Scoring Note: Examples of appropriate labels for the tension force include $F_{\text {string }}, F_{\mathrm{s}}, F_{T}$ , $F_{\text {Tension }}$ , "string force," or "tension force."

Total for part (a)

3 points

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Covered syllabus points

Question 1

Question 2