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sol9 - HW Solutions 9 8.01 MIT Prof Kowalski Rigid Body...

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HW Solutions # 9 - 8.01 MIT - Prof. Kowalski Rigid Body Rotation and Angular Momentum. 1 ) 9.78 Please refer to figure 9.29 p.358. From the definition: I = r 2 dm we observe that if an object is more concentrated around the line has less moment of inertia.(Of course this conclusion is not right if they have different masses) a ) The cylinder’s mass (object A in the figure) is the most concen- trated near its axis Object A has the smallest moment of inertia. b ) The cylinder with a hole has greater I than a cylinder (of the same mass) but slightly less than a hoop. With the assumption that it’s a thin cylinder we assume it’s very close to I of a hoop: I thin cylinder MR 2 . The cube has moment of inertia I cube = 1 12 M ( a 2 + b 2 ) = 2 3 MR 2 which is less than the thin cylinder. So, the thin cylinder (object B in the figure) has the largest moment of inertia. c ) The sphere is more concentrated near its axis than even the cylinder so it will replace solid cylinder as the smallest moment of inertia. 1
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2 ) 9.80 The key to this problem is to set up the energy conservation equation having in mind that no non-conservative force is present here: K 1 + U 1 = E 1 = E 2 = K
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