Question

A wheel, starting from rest, rotates with a constant angular acceleration of 1.90 rad/s^2. During a certain 8.00 s interval, it turns through 120 rad. How long had the wheel been turning before the start of the 8.00 s interval? What was the angular velocity of the wheel at the start of the 8.00 s interval?

Answer 1

a )

given

initial angular velocity = 0

angular acceleration $\alpha$ = 1.9 rad/sec²   

a certain time of 8 sec interval angular displacement is 120 rad

to find the time

using equation

d = $\omega$ X t + 1/2 $\alpha$ t²

120 = $\omega$ X 8 + 1/2 X 1.9 X 8²  

$\omega$ = 7.4 rad/sec

$\alpha$ = 1.9 rad/sec²

angular acceleration $\alpha$ = $\omega$ / t

t = $\omega$ / $\alpha$

t = 7.4 / 1.9

t = 3.89 sec

b )

d = $\omega$ X t + 1/2 a t²

120 = $\omega$ X 8 + 1/2 X 1.9 X 8²  

$\omega$ = 7.4 rad/sec