Question

A wheel has a constant angular acceleration of 4.5 rad/s2. during a certain 5.0 s interval, it turns through an angle of 128 rad. assuming that the wheel started from rest, how long has it been in motion at the start of this 5.0 s interval?

Answer 1

The solution for this problem is through this formula:Ø = w1 t + 1/2 ã t^2 
where:Ø - angular displacement w1 - initial angular velocity t - time ã - angular acceleration 
128 = w1 x 4 + ½ x 4.5 x 5^2 128 = 4w1 + 56.254w1 = -128 + 56.25 4w1 = 71.75w1 = 71.75/4
w1 = 17.94 or 18 rad s^-1 
w1 = wo + ãt 
w1 - final angular velocity 
wo - initial angular velocity 
18 = 0 + 4.5t t = 4 s