A wheel is rotating with an angular speed of 20 rad / s . It is stopped to rest by applying a constant torque in 4 s . If the moment of inertia of the wheel about its axis is 0.20 ~kg / m ^2 , then the work done by the torque in two seconds will be

Step-by-step solution

₁=20 rad / s , =0, t=4 ~s . So angular retardation = ₁- ₂ t = 20 4 =5 rad / s ^2 Now, angular speed after 2s ₂= ₁- t=20-5 2=10 rad / s Work done by torque in 2 ~s = loss in kinetic aligned energy & = 1 2 / ( ₁ ^2- ₁^2 )= 1 2 (0.20) ((20)^2-(10)^2 ) & = 1 2 (0.20)(400-100) & = 1 2 (0.20) (300)= 1 2 60=30 aligned