A pulley, with a rotational inertia of 2.0 10-3 kg·m2 about its axle and a radius of 20 cm, is acted on by a force applied tangentially at its rim. The force magnitude varies in time as F = 0.50t + 0.30t2, where F is in Newtons and t in seconds. The pulley is initially at rest.
(a) At t = 4.0 s what is its rotational acceleration?
(b) At t = 4.0 s what is its rotational speed?
Torque = I * alpha
Torque = |r||F|sin(theta)
The Attempt at a Solution
I have only tried part a. What I did was since I know the radius = .020 m, F, and I, I rearranged the formulas like so:
alpha = Torque / I
Since it's tangent, sin(90) = 1 therefore Torque = r*F
F at 4s = 6.8 N and multiplying this by the radius .020 m gives a torque of .136 Nm
So now alpha = .136 Nm / .002 kgm^2 = 68 rad/s^2
I plugged that in on webassign and it was wrong so apparently I'm not doing something right. Any guidance is appreciated, thanks.