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

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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 defnition: I = ± r 2 dm we observe that i± an object is more concentrated around the line has less moment o± inertia.(O± course this conclusion is not right i± they have di²erent masses) a ) The cylinder’s mass (object A in the fgure) is the most concen- trated near its axis Object A has the smallest moment o± inertia. b ) The cylinder with a hole has greater I than a cylinder (o± 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 o± a hoop: I thin cylinder MR 2 . The cube has moment o± inertia I cube = 1 12 M ( a 2 + b 2 )= 2 3 2 which is less than the thin cylinder. So, the thin cylinder (object B in the fgure) has the largest moment o± inertia. c ) The sphere is more concentrated near its axis than even the cylinder so it will replace solid cylinder as the smallest moment o± 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 =
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## This note was uploaded on 04/22/2011 for the course PHYS 1441 taught by Professor White during the Spring '08 term at UT Arlington.

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

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