A pulsar is a rapidly rotating neutron star that emits a radio beam the way a li

Question

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 = 0.0567 s that is increasing at the rate of 5.84 x 10-7 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 1190 years ago. Assuming constant , find the initial T.

Explanation / Answer

Period, T = 0.0567s,
so its angular velocity (measured in radians per second) and given by the letter w(say) is:

w = 2pi / 0.0567 = (approx) 110.814pi (radians per sec)

The problem is to find the angular acceleration - how much this angular velocity increases per second. We know that the period increases by a small amount per year, so work out how man y seconds in a year, and use that to calculate the acceleration.

seconds in 1 year = 110*60*24*365.25 (approx) = 57855600
yearly increase in period = 5.84 x 10^-7 seconds
w after 1 year = 2pi / (0.0567 + 5.84 x 10^-7) = 110.813pi

so yearly decrease in w = (110.814 - 110.813)pi = 1*10^-3pi (radians per year)

and finally ang accel is this increase divided by the number of seconds

ang accel = 10^-3*pi / 57855600 = 5.43 x 10^-11 (radians per sec)


How long till it stops?
time = speed / accel = 110.814pi / 10^-3 pi (years)
ie. time = 110814 years

Hmm....will it stop, and then start to rotate backwards? :-)

Initial speed?
1190is 953 years ago

so original speed = 110.814 pi + (10^-3pi x 953)
=
= 349.085 radians per sec

With a period of T = 2pi/260.8 = 0.017999 sec

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