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AP Physics 1: Algebra-Based 6.4 A Describe the Behavior of a System Using Conservation of Angular Momentum Questions

Apply angular momentum conservation to changing mass distributions, rotational collisions and interacting components when external torque is absent.

Syllabus
Effective Fall 2024
Course
AP Physics 1: Algebra-Based

Exam points

  • decide whether total angular momentum is conserved by checking external torque on the selected system
  • predict or derive angular-speed changes as mass moves inward or outward and rotational inertia changes
  • solve the angular speed and rotation direction after sticking or rebounding rotational collisions
  • apply equal and opposite angular-momentum changes to components interacting within a system
  • distinguish conserved angular momentum from quantities such as speed, period, inertia or kinetic energy

AP Physics 1: Algebra-Based 6.4 A Describe the Behavior of a System Using Conservation of Angular Momentum Questions 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.

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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
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