A solid body rotates an angle θ about a stationary axis according to the law θ = 6 t - 2 t 3 . What is the mean value of angular velocity (in rad   s - 1 ) over the time interval between t = 0 and the time till the body comes to rest?

Step-by-step solution

Given, θ = 6 t - 2 t 3 ...(i) ∴ d θ d t = ω = 6 - 6 t 2 As, ω = 0 (given) 6 - 6 t 2 = 0 t 2 = ± 1 As, t = - 1 s is not possible, hence t = 1 s . Substituting t = 1 s in Equation (i), we get θ 1 = 6 - 2 = 4 r a d and θ 0 = 6 × 0 - 2 × 0 2 t = 0 = 0 ∴ Mean value of ω = θ 1 - θ 0 t 1 - t 0 = 4 - 0 1 - 0 = 4 r a d s - 1