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I found the angular velocity to be 33.07 rad/s, I found this by 1/T*2PI

Now I need to solve the angular velocity. I tried using the rotational kinematic equation:

Wf = Wi + alpha * t

where:

Wf = angular velocity final

Wi = angular velocity initial

alpha = angular acceleration

t = time

Since the period of rotation is increasing by 0.00000380 s/y I added this to 0.19 and then found the Wf by take 1/.19000380 *2PI

I used the angular velocity that I already solved for Wi, the 33.07 rad/s

then for the time, it would be 1 year right? But does this need to be in seconds?

So I plugged these into the equation and solved for alpha

(Wf - Wi)/t = alpha

(33.068rad/s-33.069rad/s)/31556926s = -3.1689x10^-11 rad/s^2

But this is not the correct answer. Any advice?