Two thin rectangular sheets (0.06 m * 0.46 m) are identical. In the first sheet the axis of rotation lies along the 0.06 m side, and in the second it lies along the 0.46 m side. The same torque is applied to each sheet. The first sheet, starting from rest, reaches its final angular velocity in 7.4 s. How long does it take for the second sheet, starting from rest, to reach the same angular velocity?
2006-11-19 17:44:06 · 1 answers · asked by Alan l 1 in Science & Mathematics ➔ Physics
The moment of inertia of a rectangular plane is (1/3)*M*L^2, where M is its mass and L is the length of the plane measured from the axis of rotation. The masses of the sheets are the same, but in the first case, L = 0.46 m, and in the second case, L = 0.06 m; the rotational acceleration is given by T = I*a; the time to reach an angular velocity w is w/a, so the time is given by t = w*I/T The I for the second case is (0.06/0/46)^2 times that of the first, so the time ratio is also that. Therefore the time required for the second is
7.4*(0.06/0/46)^2
2006-11-19 17:54:14 · answer #1 · answered by gp4rts 7 · 2⤊ 0⤋