A disc of mass 25 ~kg and radius 0.2 ~m is rotating at 240 r.p.m. A retarding torque brings it to rest in 20 ~s . If the torque is due to a force applied tangentially on the rim of the disc, then the magnitude of the force in newton is

Step-by-step solution

Using rotational kinematic equation, aligned & = ₀-a t & 0= ₀-a t & = ( ₀ t ) aligned We know torque is given by, F R= Torque =I and the moment of inertia is given by, I= M R^2 2 F= I R = ( M R^2 2 ) ( 1 R ) ( ₀ t )= ( M R ₀ 2 t ) Given, M=25 ~kg , R=0.2 ~m , ₀= 240(2 ) (60) sec and t=20 sec aligned & F= (25 ~kg ) (0.2 ~m ) (8 sec ⁻¹ ) (2 20 sec ) & F= N aligned