AP Physics 1 6.3: Angular Momentum

Describe angular momentum about a chosen axis and relate it to rotational inertia, angular velocity, mass, speed, and position.

[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)

Suppose the rod is much more massive than the disk. To give the rod as much angular speed as possible, should the student make the disk hit the rod to the left of point C, at point C, or to the right of point C ? To the left of C At C To the right of C
Briefly explain your reasoning without manipulating equations.

[ 1 ]

(b)

On the Internet, a student finds the following equation for the postcollision angular speed $\omega$ of the rod in this situation: $\omega=\frac{m_{\text {disk }} x v_{0}}{I}$ . Regardless of whether this equation for angular speed is correct, does it agree with your qualitative reasoning in part (a) ? In other words, does this equation for $\omega$ have the expected dependence as reasoned in part (a) ? Yes No
Briefly explain your reasoning without deriving an equation for $\omega$ .

[ 2 ]

2 points
Correct answer: "Yes"
If "No" is selected, the explanation may still earn full credit if an incorrect selection was made in part (a).
For a selection consistent with the selection from part (a)
For indicating that the equation shows that $\omega$ increases with increasing x
Example: According to the equation, $\omega$ increases with x; a bigger x produces a bigger angular speed. This agrees with my reasoning from part (a), where I said a bigger x creates a bigger angular speed after the collision.

(c)

Another student deriving an equation for the postcollision angular speed $\omega$ of the rod makes a mistake and comes up with $\omega=\frac{I x v_{0}}{m_{\text {disk }} d^{4}}$ . Without deriving the correct equation, how can you tell that this equation is not plausible-in other words, that it does not make physical sense? Briefly explain your reasoning.

For parts (d) and (e), do NOT assume that the rod is much more massive than the disk.

[ 3 ]

3 points
For focusing on functional dependence (instead of, for example, considering units/dimensions)
For addressing $m_{\text {disk }}, I$ , or both
For correctly concluding that the equation is wrong because of the dependence on $m_{\text {disk }}, I$ , or both
Example: If $m_{\text {disk }}$ is large, then more angular momentum will be transferred during the collision. But the equation shows the angular speed decreasing with increasing $m_{\text {disk }}$ , because it is in the denominator.

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6.3.A—Describe the angular momentum of an object or rigid system question 1

Question (a)

Question (b)

Question (c)