A disc of radius 10cm is rotating about the central axis perpendicular to its plane. A force of 5N acts on it tangentially. The disc was initially at rest. Calculate the value of power supplied by the force when the disc has rotated by 30°.The mass of the disc is 2kg.
Correct Answer: 1.8W
Work done = Tθ, where T is torque & θ is angular displacement. T = r*F = 0.1*5 = 0.5Nm & θ = 30° = π/6 rad. ∴ Work = 0.5*π/6 = π/12 J. Moment of inertia about spinning axis = MR2/2 = 2*0.01/2 = 0.01kgm2. Using, T = Ia, where ‘I’ is moment of inertia & ‘a’ is angular acceleration, we get: a = T/I ∴ a = 0.5/0.01 = 50 rad/s2. Now, θ = w0t + (1/2)at2 to calculate the time for 30° rotation, where wo is initial angular velocity. ∴ π/6 = 0 + 0.5*50*t2. ∴ t = √(π/150) = 0.145 s. ∴ Power = Work/time = (π/12) / (0.145) = 1.8 W.