AP Physics 1 5.4.A: Rotational Inertia of a Rigid System

Practise AP Physics 1 rotational inertia by tracing how moving mass relative to an axis changes a rigid system’s inertia and angular speed.

Exam points

Estimate angular-speed changes when mass moves outward, and justify them from increased rotational inertia.

[Maximum number: 1]

8 points; suggested time: 15-20 minutes

A mass m is initially resting at the center of a rotating disk with

rotational inertia $(1 / 2) M R^{2}$ . The entire system is freely rotating with an

initial angular speed of $w_{0}$ . As time goes by, the mass is carefully

moved at a constant speed outward from the center. This is done in

such a way that no torque on the system is introduced.

(a) If the mass m is about half the mass of the spinning disk, estimate

the approximate angular speed of the two-mass system after the

mass m has been pushed all the way to the edge in terms of $w_{0}$ .

Justify your estimate using qualitative reasoning beyond

referencing equations.

4. (a) 1 point. Pushing the mass out to the edge will result in an increase

in the rotational inertia of the system of $m r^{2}$ or $(M / 2) r^{2}$ , which is

same as the original rotational inertia of the disk alone.

1 point. Since this is effectively doubling the rotational inertia, the

angular speed should be reduced to 1/2 of its original value.

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