F=ma 2024 Problem 19

Physics · mechanics

Problem

Question: A wheel of radius

R

has a thin rim and four spokes,each of which have uniform density.As shown in the figure, the entire rim has mass

m

, three of the spokes each have mass

m

, and the fourth spoke has mass

3m

. The wheel is suspended on a horizontal frictionless axle passing through its center. If the wheel is slightly rotated from its equilibrium position, what is the angular frequency of small oscillations? (A)

\sqrt{\frac{g}{3R}}

. (B)

\sqrt{\frac{g}{2R}}

. (C)

\sqrt{\frac{2g}{3R}}

. (D)

\sqrt{\frac{g}{R}}

. (E)

\sqrt{\frac{7g}{6R}}

. *Note: This problem references figure(s): `image_question/F=MA_2024_19_1.png`*

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