Angular acceleration of a pulsar

[vertex78]

A pulsar is a rapidly rotating neutron star that emits radio pulses with precise synchronization, there being one such pulse for each rotation of the star. The period T of rotation is found by measuring the time between pulses. At present, the pulsar in the central region of the Crab nebula has a period of rotation of T = 0.19000000 s, and this is observed to be increasing at the rate of 0.00000380 s/y.

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?

 

[Doc Al]

(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?

Your error is in rounding off your values for W. Use many more significant figures in your calculator and you get a better estimate for the change in W.