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 = 0.0220 s that is increasing at the rate of 1.05 x 10-6 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) Suppose the pulsar originated in a supernova explosion seen 890 years ago. Assuming constant alpha, find the initial T.

Explanation / Answer

a)

angular speed

W=2pi/T

dW/dt =-(2pi/T2)(dT/dt)

for the pulsar

dT/dt =1.05*10-5 s/year =1.05*10-5/(365*24*60*60)

dT/dt=3.33*10-13

angular acceleration of pulsar is

alpha =dW/dt =(-2pi/0.0222)(3.33*10-13)

alpha=-4.32*10-9 rad/s2

b)

Present angular speed of pulsar is

W=2pi/T=2pi/0.022=285.6 rad/s

Pulsar will stop rotating at time

tf=W/alpha =285.6/4.32*10-9=6.61*1010 s

in years

tf=6.61*1010/(365*24*60*60)=2096.4 years=2097 yeras

c)

As the pulsar was formed 890 years ago ,its life till the present is 2097-890=1207 years ,Its period of rotation at the time of its birth is

Ti=(0.022-1.05*10-5*1207)

Ti=0.00933 s or 9.3265*10-3 s or 9.3265 ms

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.