Answer:
a).[tex]a_p=-2.39x10^{-12} rad/s^2[/tex]
b).[tex]t=1016298.8 years[/tex]
c).[tex]T_i=80.58x10^{-3}s[/tex]
Explanation:
a).
The acceleration for definition is the derive of the velocity so:
[tex]a_p=\frac{dw}{dt}[/tex]
[tex]w=\frac{2\pi}{t}[/tex]
[tex]a_p=\frac{dw}{dt}=-\frac{2\pi}{t^2}*\frac{dT}{dt}[/tex]
[tex]dT=0.0808s[/tex]
[tex]dt=1 year*\frac{365d}{1year} \frac{24hr}{1d} \frac{60minute}{1hr} \frac{60s}{1minute}=31.536x10^{6}s[/tex]
Replacing
[tex]a_p=-\frac{2\pi}{0.082s^2}*\frac{9.84x10^{-7}}{31.536x10^{6}s}= -2.39x10^{-12} rad/s^2[/tex]
b).
If the pulsar will continue to decelerate at this rate, it will stop rotating at time:
[tex]t=\frac{w}{a_p}[/tex]
[tex]w=\frac{2\pi }{t}=\frac{2\pi }{0.0820s}=76.62 rad/s[/tex]
[tex]t=\frac{76.62 rad/s}{2.39x10^{-12}rad/s^2}= 3.2058x10^{13}s[/tex]
[tex]t=1016298.8 years[/tex]
c).
582 years ago to 2019
1437
[tex]T_i=0.0820-9.84x10^{-7}*1437)=80.58x10^{-3}s[/tex]