A uniform solid disc of mass 4 kg and radius 0.5 m is pivoted at its centre and is initially at rest. A constant tangential force of 10 N is applied to its rim. What will be the angular velocity of the disc after 3 s ?

Step-by-step solution

The moment of inertia of a uniform solid disc about its central axis is: I = 1 2 MR^2 = 1 2 4 (0.5)^2 = 2 0.25 = 0.5 kg m ^2 The torque produced by the tangential force applied at the rim is: = F R = 10 0.5 = 5 N m Using Newton's second law for rotation, the angular acceleration is: = I = 5 0.5 = 10 rad/s ^2 Since the disc starts from rest ( _i = 0 ), the final angular velocity after t = 3 s is: _f = _i + t = 0 + (10 3) = 30 rad/s Answer: 30 rad/s