AP Physics 1 6.4: Conservation of Angular Momentum

Analyze angular momentum for a selected system and determine when external interactions change the total angular momentum about an axis.

[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 $m_{\text {disk }}$ toward the rod with velocity $v_{0}$ 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.

(a)

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

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4 points

For using an expression of conservation of angular momentum for the disk and rod
Note: This point is not awarded for equating angular and linear momentum.

1 point

For indicating that the initial angular momentum of the system is equal to $m_{\text {disk }} v_{0} x$

1 point

For a dimensionally correct expression for the post-collision angular momentum that
includes $I \omega$

1 point

For indicating the correct rotational inertia of the system after the collision: $I+m_{\text {disk }} x^{2}$

1 point

(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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6.4.A—Describe the behavior of a system using conservation of angular momentum question 1

Question (a)

Question (b)