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 = 0.0820 s that is increasing at the rate of 9.84 x 10-7 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 582 years ago. Assuming constant alpha, find the initial T.

Answer 1

a).
`a_p=-2.39x10^(-12) rad/s^2`

b).
`t=1016298.8 years`

c).
`T_i=80.58x10^(-3)s`

Step-by-step explanation:

a).

The acceleration for definition is the derive of the velocity so:

`a_p=(dw)/(dt)`

`w=(2\pi)/(t)`

`a_p=(dw)/(dt)=-(2\pi)/(t^2)*(dT)/(dt)`

`dT=0.0808s`

`dt=1 year*(365d)/(1year) (24hr)/(1d) (60minute)/(1hr) (60s)/(1minute)=31.536x10^(6)s`

Replacing

`a_p=-(2\pi)/(0.082s^2)*(9.84x10^(-7))/(31.536x10^(6)s)= -2.39x10^(-12) rad/s^2`

b).

If the pulsar will continue to decelerate at this rate, it will stop rotating at time:

`t=(w)/(a_p)`

`w=(2\pi )/(t)=(2\pi )/(0.0820s)=76.62 rad/s`

`t=(76.62 rad/s)/(2.39x10^(-12)rad/s^2)= 3.2058x10^(13)s`

`t=1016298.8 years`

c).

582 years ago to 2019

1437

`T_i=0.0820-9.84x10^(-7)*1437)=80.58x10^(-3)s`