# The angular acceleration and period of a pulsar

• Ursa
In summary, the conversation discussed the formula for calculating period (T) and angular velocity (ω), as well as the formula for angular acceleration (α) in the context of a changing period. The conversation also touched on the concept of infinity and how it relates to the calculation of angular acceleration. In order to correctly solve the problem, it was suggested to be more careful with substitutions and to assume a constant negative angular acceleration to find when the angular speed becomes zero. Additionally, it was mentioned that working backwards can help calculate the initial angular speed and convert it to a value of T.
Ursa
Homework Statement
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 = 0.0178 s that is increasing at the rate of 9.27 x 10-8 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 1160 years ago. Assuming constant \alpha , find the initial T
Relevant Equations
T=\frac {2\pi}{\omega}
for (a) ##T=\frac {2\pi}{\omega}##
$$\omega=\frac {2\pi}{T}$$
$$\frac{d \omega}{dt}=\frac {-2\pi}{T^2} \frac {dT}{dt}$$
$$\alpha=\frac {-2\pi}{(2.94*10^-15)^2} = 7.27*10^29 rad/s^2$$

for (b) I'm understand that it's infinity, because the period is increasing indefinitely, so it's slowing down forever.
But I don't know how to express that in formula, and infinity is not something I can input in the homework software.
So I must be wrong about it, but don't know how to get the correct answer.

(c) I don't have anything here.

a is wrong - do your substitution more carefully.
In b they are asking you to assume the angular acceleration is constant - not dT/dt. If you have a constant negative α, and know the angular speed now, you can work out when the angular speed becomes zero.
For c you can likewise work backwards and calculate what the angular speed was initially, then convert that to a value of T.

## 1. What is a pulsar?

A pulsar is a highly magnetized, rotating neutron star that emits beams of electromagnetic radiation along its magnetic poles. These beams are observed as regular pulses of radiation, hence the name "pulsar".

## 2. How is the angular acceleration of a pulsar calculated?

The angular acceleration of a pulsar can be calculated using the formula: α = 4π²/I * (M/R³), where α is the angular acceleration, I is the moment of inertia, M is the mass of the pulsar, and R is the radius of the pulsar.

## 3. What is the period of a pulsar?

The period of a pulsar refers to the time it takes for the pulsar to complete one full rotation. This can range from milliseconds to seconds, depending on the individual pulsar.

## 4. How do we measure the period of a pulsar?

The period of a pulsar can be measured using radio telescopes, which detect the regular pulses of electromagnetic radiation emitted by the pulsar. By measuring the time between these pulses, the period can be determined.

## 5. What is the significance of studying the angular acceleration and period of a pulsar?

Studying the angular acceleration and period of a pulsar can provide valuable insights into the physical properties of neutron stars, as well as the behavior of matter under extreme conditions. It can also help us better understand the evolution of stars and the formation of compact objects in the universe.

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