The angular acceleration and period of a pulsar

[Ursa]

Homework Statement

A pulsar is a rapidly rotating neutron star that emits a radio beam the way a lighthouse emits a light beam. We receive a radio pulse for each rotation of the star. The period T of rotation is found by measuring the time between pulses. Suppose a pulsar has a period of rotation of T = 0.0178 s that is increasing at the rate of 9.27 x 10-8 s/y. (a) What is the pulsar's angular acceleration ? (b) If is constant, how many years from now will the pulsar stop rotating? (c) Suppose the pulsar originated in a supernova explosion seen 1160 years ago. Assuming constant \alpha , find the initial T

Relevant Equations

T=\frac {2\pi}{\omega}

for (a) $T=\frac {2\pi}{\omega}$
$$\omega=\frac {2\pi}{T}$$
$$\frac{d \omega}{dt}=\frac {-2\pi}{T^2} \frac {dT}{dt} $$
$$\alpha=\frac {-2\pi}{(2.94*10^-15)^2} = 7.27*10^29 rad/s^2$$

for (b) I'm understand that it's infinity, because the period is increasing indefinitely, so it's slowing down forever.
But I don't know how to express that in formula, and infinity is not something I can input in the homework software.
So I must be wrong about it, but don't know how to get the correct answer.

(c) I don't have anything here.

 

[mjc123]

a is wrong - do your substitution more carefully.
In b they are asking you to assume the angular acceleration is constant - not dT/dt. If you have a constant negative α, and know the angular speed now, you can work out when the angular speed becomes zero.
For c you can likewise work backwards and calculate what the angular speed was initially, then convert that to a value of T.