Question

Two thin rectangular sheets (0.29 m 0.40 m) are identical. In the first sheet the axis of rotation lies along the 0.29-m side, and in the second it lies along the 0.40-m side. The same torque is applied to each sheet. The first sheet, starting from rest, reaches its final angular velocity in 7.7 s. How long does it take for the second sheet, starting from rest, to reach the same angular velocity?

Answer 1

Moment of intertia is proportional to the square of the dimension perpendicular to the axis of rotation. It is therefore (40/29)^2 = 1.902 times higher when the axis is the 0.29 m side. That would be the first sheet.

When the same torque is applied, the angular acceleration in inversely proportional to moment of inertia.

Angular velocity is proportional to the angular acceleration.

The second sheet wil take 1/1.902 times as long to attain the same angular velocity as the first.