A rotating wheel requires 9.00 s to rotate 29.0 revolutions. Its angular velocity at the end of the 9.00 s interval is 98.0 rad/s. What is the constant angular acceleration of the wheel in radians/second squared? (Do not assume that the wheel starts at rest.)

Answer 1

displacement=Wi*t+1/2 alpha*t^2

where alpha is the angular acceleration in rev/sec

you know:
29=wi*9+1/2 alpha*81

and you know
wf=98/2PI rev/sec=wi+alpha*9

wi= 98/2PI-alpha*9
putting that in to the first equation
29=(98/2PI-alpha*9)*9 +1/2 alpha*81
solve for alpha. Now this alpha will be in rev/s^2, in radians/sec^2, divide rev by 2PI to get that.