A particle is moving with constant angular acceleration 4 , rad/s ^2 in circular path. At what time the magnitudes of its tangential acceleration and centripetal acceleration will be equal ?

Step-by-step solution

Given angular acceleration = 4 rad/s ^2 . Tangential acceleration is given by a_t = r . Centripetal acceleration is given by a_c = r ^2 . Equating the magnitudes of tangential and centripetal acceleration: a_t = a_c r = r ^2 ^2 = Assuming the particle starts from rest, the angular velocity at time t is = t . Substituting in the above equation: ( t)^2 = ^2 t^2 = t^2 = 1 Substituting = 4 rad/s ^2 : t^2 = 1 4 t = 0.5 s Answer: 0.5 s