Pulsar Radius from its rotational period

[TFM]

Homework Statement

A pulsar emits bursts of radio waves with a period of 10 ms. Find an upper limit to the radius of the pulsar.

Homework Equations

Not Sure

The Attempt at a Solution

Can anyone help with this, I cannot see how the period will help tell you the upper limit to the radius. I know that pulsars are basically neutron stars, and they have high densities (10^15 kg/m^3), but I ams lightly unsure how to get the radius of the pulsar from its period.

Any helpful suggestions would be most helpful,

Thanks in advanced,

TFM

 

[mgb_phys]

What happens when the rotation rate is fast enough that centrifugal force on a point on the surface as is stronger than gravity?

 

[TFM]

Well, Gravity is pulling down, the centrifugal force is pushing outwards, so items on the surface would be "pushed" off of the surface.

 

[mgb_phys]

Correct - so at a certain speed the surface would break off, doesn't this set a maximum radius for a given rotation rate?

 

[TFM]

Indeed it would,

So:

$$mg = m\omega^2r$$

$$g = \omega^2r$$


And since:

$$Omega = \frac{2\pi}{Period}$$

Thus:

$$g = \frac{4\pi^2}{Period^2}r$$

Does this look okay?

 

[mgb_phys]

You will need to write 'g' for the star in terms of it's mass (or density) and radius.

 

[TFM]

True, but we aren't given a mass for the star? Would we use the density as being 10^15?

 

[TFM]

Okay, so if we use:

$$g = -\frac{MG}{r^2}$$

and

$$M = density*volume$$

$$M = density*(\frac{4}{3}\pi r^3)$$

$$g = -\frac{(density*(\frac{4}{3}\pi r^3))G}{r^2}$$


Thus:

$$-\frac{(density*(\frac{4}{3}\pi r^3))G}{r^2} = \frac{4\pi^2}{Period^2}r$$

Since we need the magnitude only for g:

$$\frac{(density*(\frac{4}{3}\pi r^3))G}{r^2} = \frac{4\pi^2}{Period^2}r$$

$$(density*(\frac{4}{3}\pi ))G = \frac{4\pi^2}{Period^2}$$

Does this look better?

TFM