Question

A disk is free to rotate on a fixed axis. A force of given magnitude F, in the plane of the disk, is to be applied. Of the following alternatives the greatest angular acceleration is obtained if the force is: A) applied tangentially halfway between the axis and the rim B) applied tangentially at the rim C) applied radially halfway between the axis and the rim D) applied radially at the rim E) applied at the rim but neither radially nor tangentially

Please explain why it's A and not the others.

Answer 1

Torque T = r×F = (moment of inertia)(angular acceleration)

=) Angular acceleration = rF Sin(theta)/moment of inertia

=) Angular acceleration = 2rF.Sin(theta)/mr^2 = 2F.Sin(theta)/mr

That means angular acceleration is directly proportional to Sin(theta) and inversely proportional to radius

For greater angular acceleration, radius should be minimum and Sin(theta) should be maximum..

For radial direction theta = 90°, that means sin90 = 1

Hence option A.) is correct choice .

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