Unformatted text preview: is I b = (1/12)ML 2 . a) What is the rotational inertia of the rigid structure about the rotational axis? Since the structure consists of a hoop and square, the total rotational inertia is I tot = I H + I S According to the parallel axis theorem, the rotational inertia of the hoop about the axis through its rim is I H = (1/2)mR 2 + mR 2 = (3/2)mR 2 = 1.47 kg · m 2 The square consists of a rod along the axis, two rods with the axis at one end and a rod a distance L away from the axis. The parallel axis theorem yields I S = 0 + 2 × [(1/12)ML 2 + (1/2)ML 2 ] + ML 2 = (5/3)ML 2 = 1.60 kg · m 2 The rotational inertia of the structure is I tot = I H + I S = 3.07 kg · m 2 b) What is the angular momentum about the rotational axis? The angular velocity of the structure is ω = 2 π /T = 1.26 rad/s By definition, the angular momentum of the structure is l = I tot ω = 3.86 kg · m 2 /s...
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This note was uploaded on 12/10/2011 for the course PHY 2048 taught by Professor Field during the Spring '08 term at University of Florida.
- Spring '08