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A disc of mass m, and radius r, is spinning at an angular velocity of ω....

A disc of mass m, and radius r, is spinning at an angular velocity of ω. A force, F, is applied at the edge of the disc, in a direction tangential to the discs circumference. The force is applied for a total time t. What is its equation for final angular velocity?

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Answer #1

If the force acts tangentially to the disc then the torque acting on the disc is Fr.

Torque produces angular acceleration and hence Fr = I , where I is moment of inertia of disc about its natural axis. I = mr2 / 2. Then Fr = mr2 / 2. Hence = 2F / mr

The relation between angular velocity and angular acceleration is

If force is applied in the direction of initial angular velocity then is positive and if the force is applied in the direction opposite to initial angular velocity then is negative

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