Question

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 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 = 0.09000000 s, and this is observed to be increasing at the rate of 0.00000467 s/yr. What is the angular velocity of the star?What is the angular acceleration of the pulsar?If its angular acceleration is constant, in how many years will the pulsar stop rotating?The pulsar originated in a super-nova explosion in the year A.D. 1054. What was the period of rotation of the pulsar when it was born?

Answer 1

W = 2 pi / T if W is angular velocity.
so W = 2 pi / .09 = 69.8 radians/second
Tin one year - T now = 4.67*10^- 6 seconds
but one year = 3600*24*365 = 3.15*10^7 seconds
so change of T per second = 4.67*10^-6 / 3.15*10^7
= 1.48 *10^-13 seconds/second = dT/dt
Now Either I do some calculus or you convert all that to angular velociteies by brute force.
I have dT/dt
I want dW/dt
but
W = 2 pi/T
dW/dT = 2 pi (-dT/dt)/T^2 =
2 pi (-1.48*10^-13) / (.09)^2
so angular accleration = dW/dt = a
a= - 1148 * 10^-13 radians /s^2
or
a= - 1.15 * 10^-10 radians/s^2
now you have the initial angular velocity and the angular acceleration and the number of seconds per year. I think you can take it from there