F=ma 2025 Problem 15

Physics · mechanics

Problem

Question: As shown in the figure, a uniform rigid rod of mass

M

and length

2L

is attached to a massless rod of length

L

, which is fixed at one end to the ceiling and free to rotate in a vertical plane. The massive rod is connected to the free end of the massless rod. Suppose an impulse

J

is applied horizontally to the bottom of the massive rod. Determine the relationship between the magnitudes of the angular velocity

\omega

of the massless rod and

\Omega

of the massive rod immediately after the impulse is applied. The moment of inertia of a uniform rod of length

d

and mass

m

about its center of mass is given by

I = \frac{1}{12}m{d}^2

. (A)

\Omega = \frac{3}{4}\omega

. (B)

\Omega = \frac{2}{3}\omega

. (C)

\Omega = \frac{4}{3}\omega

. (D)

\Omega = \frac{1}{12}\omega

. (E)

\Omega = \frac{3}{2}\omega

. *Note: This problem references figure(s): `image_question/F=MA_2025_15_1.png`*

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