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The same force is applied to the edge of two hoops (see the drawing). The hoops have the same mass, whereas the radius of the larger hoop is twice the radius of the smaller one. The entire mass of each hoop is concentrated at its rim, so the moment of inertia is I = Mr2, where M is the mass and r is the radius. Which hoop has the greater angular acceleration, and how many times as great is it compared to the angular acceleration of the other hoop?
(a) The smaller hoop; two times as great
(b) The smaller hoop; four times as great
(c) The larger hoop; two times as great
(d) The larger hoop; four times as great
(e) Both have the same angular acceleration. |
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