Halliday, Resnick & Walker — Rotation: Problem 18

18 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. The pulsar in the Crab nebula has a period of rotation of $T = 0.033\text{ s}$ that is increasing at the rate of $1.26 \times 10^{-5}\text{ s/y}$. (a) What is the pulsar’s angular acceleration $\alpha$? (b) If $\alpha$ is constant, how many years from now will the pulsar stop rotating? (c) The pulsar originated in a supernova explosion seen in the year 1054. Assuming constant $\alpha$, find the initial $T$.