AP Physics 1: Algebra-Based 6.4 Conservation of Angular Momentum Questions

Analyse angular momentum for a selected system, then apply conservation to changing mass distributions, collisions and internal transfers.

Exam points

select a system boundary and decide whether external torque changes its total angular momentum
apply Iω conservation to derive speed changes as mass distribution or orbital radius changes
solve angular speed and direction after sticking or rebounding rotational collisions
track equal and opposite angular-momentum transfers between interacting system components
distinguish conserved angular momentum from changing inertia, speed, period or kinetic energy

Covered syllabus points

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

[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.

[ 4 ]

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

[ 2 ]

[Maximum number: 4]

Figure for 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.

(a)

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 ]

(b)

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 $I_{1}$ , 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 $I_{2}$ , and the disk completes one rotation every 2.0 s.

[ 2 ]

(i)

Figure 1

Figure 2

Derive an equation for $I_{2}$ in terms of $I_{1}$ .

[ 2 ]

(c)

i. 2 points

For using an equation expressing the conservation of angular momentum with I and $\omega$

$I_{2} \omega_{2}=I_{1} \omega_{1}$

For correctly substituting the angular speed values and obtaining a correct answer or an

algebraic equivalent of the correct answer

$I_{2}=\frac{I_{1} \omega_{1}}{\omega_{2}}=\frac{I_{1}(1 / 2.5)}{(1 / 2)}$

$I_{2}=\frac{4}{5} I_{1}$

1 point

All question bank results loaded

Covered syllabus points

Question 1

Question (a)

Question (b)

Question 2

Question (a)

Question (b)

Question (i)