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AP Physics 1 6.4 Angular Momentum Conservation Overview

Analyze angular momentum for a selected system and determine when external angular impulse changes its total angular momentum about an axis.

Syllabus
Effective Fall 2025
Course
AP Physics 1: Algebra-Based

Exam points

  • Apply angular-momentum conservation when the net external angular impulse on a system is zero.
  • Explain how an external interaction changes total angular momentum about the selected axis.

Covered syllabus points

6.4.A—Describe the behavior of a system using conservation of angular momentum6.4.B—Describe how the selection of a system determines whether the angular momentum of that system changes. AP…

6.4 Conservation of Angular Momentum question 1

[Maximum number: 6]

(12 points, suggested time 25 minutes)
The left end of a rod of length d and rotational inertia I is attached to a frictionless horizontal surface by a frictionless pivot, as shown above. Point C marks the center (midpoint) of the rod. The rod is initially motionless but is free to rotate around the pivot. A student will slide a disk of mass mdisk m_{\text {disk }} toward the rod with velocity v0v_{0} perpendicular to the rod, and the disk will stick to the rod a distance x from the pivot. The student wants the rod

disk system to end up with as much angular speed as possible.

Question (a)

(a)

Immediately before colliding with the rod, the disk's rotational inertia about the pivot is mdisk x2m_{\text {disk }} x^{2} and its angular momentum with respect to the pivot is mdisk v0xm_{\text {disk }} v_{0} x. Derive an equation for the postcollision angular speed ω\omega of the rod. Express your answer in terms of d,mdisk ,I,x,v0d, m_{\text {disk }}, I, x, v_{0}, and physical constants, as appropriate.

[ 4 ]

Question (b)

(b)

Consider the collision for which your equation in part (d) was derived, except now suppose the disk bounces backward off the rod instead of sticking to the rod. Is the postcollision angular speed of the rod when the disk bounces off it greater than, less than, or equal to the postcollision angular speed of the rod when the disk sticks to it? Greater than Less than Equal to
Briefly explain your reasoning.

Figure for Question (b) — AP Physics 1: Algebra-Based
[ 2 ]

6.4 Conservation of Angular Momentum question 2

[Maximum number: 2]
Figure for Question 6.4 Conservation of Angular Momentum question 2 — AP Physics 1: Algebra-Based

(7 points, suggested time 13 minutes) Two ladybugs are standing on a rotating disk that is spinning counterclockwise, as shown in the figure above. Assume that friction in the bearings of the axle is negligible.

Question (a)

(a)
Figure for Question (a) — AP Physics 1: Algebra-Based

(b) Ladybug A begins walking in a circular path in the direction of the disk's rotation. Does the magnitude of the angular momentum of the disk alone (not the ladybugs-disk system) increase, decrease, or stay the same? Increase Decrease Stay the same Briefly explain your reasoning.

[ 2 ]

Question (b)

(b)
Figure for Question (b) — AP Physics 1: Algebra-Based

(c) In a different scenario, a single ladybug is standing near the edge of the disk at a distance of 0.9 R from the center, where R is the radius of the disk, as shown in Figure 1 below. The rotational inertia of the ladybug- disk system is I1I_{1}, and the disk completes one rotation in 2.5 s. The ladybug then walks toward the center of the disk to a distance of 0.1 R from the center and comes to a Now the rotational inertia of the system is I2I_{2}, and the disk completes one rotation every 2.0 s.

[ 3 ]

Question (i)

(i)
Figure 1

Figure 1

Figure 2

Figure 2

Figure for Question (i) — AP Physics 1: Algebra-Based

i. Derive an equation for I2I_{2} in terms of I1I_{1}.

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