Two thin rectangular sheets (0.23 m 0.37 m) are identical. In the first sheet th
ID: 1494738 • Letter: T
Question
Two thin rectangular sheets (0.23 m 0.37 m) are identical. In the first sheet the axis of rotation lies along the 0.23-m side, and in the second it lies along the 0.37-m side. The same torque is applied to each sheet. The first sheet, starting from rest, reaches its final angular velocity in 9.5 s. How long does it take for the second sheet, starting from rest, to reach the same angular velocity? Two thin rectangular sheets (0.23 m 0.37 m) are identical. In the first sheet the axis of rotation lies along the 0.23-m side, and in the second it lies along the 0.37-m side. The same torque is applied to each sheet. The first sheet, starting from rest, reaches its final angular velocity in 9.5 s. How long does it take for the second sheet, starting from rest, to reach the same angular velocity?Explanation / Answer
The moment of inertia of a rod about one of its sides = 1/3 m L2
Ratio of moments of inertia = [1/3 m 0.232] / [ 1/3 m 0.372] = 0.386
Torque = moment of inertia * angular acceleration
ang vel = time * angular acceleration
= 9.5 * 64 = 3.67 s
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