A wheel, starting from rest, has a constant angular acceleration of 1.3 rad/s2. In a 2.5-s interval, it turns through an angle of 98 rad. How long has the wheel been in motion at the start of this 2.5-s interval?

Answer 1

W = Wo + a t
T = To + Wo t + (1/2) a t^2
same old equations but now T is theta, the angle, W is angular velocity, and a is angular acceleration
so
Here To is zero, initial angle, Wo = 0, initial speed
T = .65 t^2 at start of interval
98 + T = .65 (t+2.5)^2
subtract the first from the second
98 = (.65)(5 t+6.25)
98 = 3.25 t + 4.06
t = 28.9 seconds
Check my arithmetic!!!
W = Wo + a T