A wheel having moment of inertia 40 kgm ^2 about its axis, rotates at 50 rpm . The angular retardation required to stop this wheel in 90 ~s is rads ⁻² .

Step-by-step solution

Given, moment of inertia, I =40 ~kg - m ^2 Initial angular frequency, _i=50 rpm = 50 2 60 = 5 3 rads ⁻¹ Final angular velocity, _f=0 rads ⁻¹ Time, t=90 ~s Let, be the angular retardation and since, _f- _i= t Therefore, = _f- _i t = 0- 5 3 90 = - 3 18 = - 54 rad s ⁻² Hence, negative sign is for retardation.