A disc is free to rotate about an axis.A force applied at a distance d from the axis causes an angular acceleration $\alpha$.What angular acceleration is produced if the same force is applied a distance 2d from the axis?
A)$\alpha$
B)2$\alpha$
C)$\alpha$/2
D)4$\alpha$
E)$\alpha$/4

Question

Quizplus · Accepted Answer

The torque applied is equal to the force times the perpendicular distance from the axis. So, if the distance is doubled, the torque will be twice as much. The moment of inertia of the disc is also proportional to the square of the distance from the axis of rotation, so if the distance is doubled, the moment of inertia will be four times as much. Therefore, the angular acceleration will be given by:
α2 = (F1·2d)/(4I1) = F1d/(2I1) = 2F1d/(4I1) = 2α1.

A Disc Is Free to Rotate About an Axis α\alphaα What Angular Acceleration Is Produced If the Same Force Is

A Disc Is Free to Rotate About an Axis $\alpha$ What Angular Acceleration Is Produced If the Same Force Is