A wheel rotating about a fixed axis through its center has a

A wheel rotating about a fixed axis through its center has a constant angular acceleration of 4.0 rad/s¬2. In certain 4.0 s interval the wheel turns through an angle of 80 rads. (a) What is the angular velocity of the wheel at the start of the 4.0 s interval? (b) Assuming that the wheel starts from rest, how long is it in motion at the start of the 4.0 s interval?

Solution

a)
a = 4 rad/s^2
t = 4 s
d = 80 rad
use:
d = wi*t + 0.5*a*t^2
80 = wi*4 + 0.5*4*(4)^2
wi = 12 rad/s
Answer: 12 rad/s
b)
use:
wf = wi+a*t
12 = 0 + 4*t
t= 3s
Answer: 3s