Constant angular acceleration

[shadowice]

Homework Statement

A pulsar is a rapidly rotating neutron star that emits radio pulses with precise synchronization, there being one such pulse for each rotation of the star. The period T of rotation is found by measuring the time between pulses. At present, the pulsar in the central region of the Crab nebula has a period of rotation of T = 0.16000000 s, and this is observed to be increasing at the rate of 0.00000506 s/y.

If its angular acceleration is constant, in how many years will the pulsar stop rotating?
already found
angular acel to be -3.935x10^-11 rad/s^2
wf = 39.269
wi = 39.2699

Homework Equations

The Attempt at a Solution

Im stumped as to how to find this, i had initially tried to use wf = wi + angular accel*t thinking that the t i solved for would be the value i wanted.

i did 39.269 = 39.2699+ -3.935x10^-11t
that gave me 31559593.39 seconds then i did conversions to turn s into yrs which was that /60 s /60 min/24 hr/365d = 1.0007 yrs which is way to small it should be thousands of years shouldn't it.

 

[alphysicist]

Hi shadowice,

Homework Statement

A pulsar is a rapidly rotating neutron star that emits radio pulses with precise synchronization, there being one such pulse for each rotation of the star. The period T of rotation is found by measuring the time between pulses. At present, the pulsar in the central region of the Crab nebula has a period of rotation of T = 0.16000000 s, and this is observed to be increasing at the rate of 0.00000506 s/y.

If its angular acceleration is constant, in how many years will the pulsar stop rotating?
already found
angular acel to be -3.935x10^-11 rad/s^2
wf = 39.269
wi = 39.2699

Homework Equations

The Attempt at a Solution

Im stumped as to how to find this, i had initially tried to use wf = wi + angular accel*t thinking that the t i solved for would be the value i wanted.

i did 39.269 = 39.2699+ -3.935x10^-11t
that gave me 31559593.39 seconds then i did conversions to turn s into yrs which was that /60 s /60 min/24 hr/365d = 1.0007 yrs which is way to small it should be thousands of years shouldn't it.

I have not checked all your numbers here, but your two angular speeds you have are the angular speed at the initial point (wi) and one year later (wf). So when you calculated the time, you got back the original time of one year.

So instead, if we want to calculate the time when the pulsar stops, what angular speeds would be used in the equation?

 

[nlightner]

I would approach this problem by using the equations of rotational motion. The period of rotation can be related to the angular velocity and angular acceleration through the equation T = 2π/ω, where ω is the angular velocity. We are given the initial and final angular velocities, as well as the angular acceleration, so we can rearrange this equation to solve for the time it takes for the pulsar to stop rotating:

T = 2π/ω
0.16000000 s = 2π/39.2699 rad/s
t = 2π/39.2699 rad/s * 0.16000000 s
t = 0.010164 s

Next, we can use the equation ωf = ωi + αt, where ωf is the final angular velocity, ωi is the initial angular velocity, α is the angular acceleration, and t is the time. We can rearrange this equation to solve for the time it takes for the pulsar to stop rotating:

ωf = ωi + αt
0 = 39.2699 rad/s + (-3.935x10^-11 rad/s^2)*t
t = -39.2699 rad/s / (-3.935x10^-11 rad/s^2)
t = 9.99x10^11 s

Finally, we can convert this time into years:

t = 9.99x10^11 s * (1 min / 60 s) * (1 hr / 60 min) * (1 d / 24 hr) * (1 yr / 365 d)
t = 31714.6 yr

Therefore, if the angular acceleration remains constant, the pulsar will stop rotating in approximately 31,714.6 years. However, it is important to note that this calculation assumes that the angular acceleration remains constant, which may not be the case in reality. Other factors such as the pulsar's interaction with its surrounding environment could affect its rotation and make this estimate inaccurate.