Centripetal acceleration of Neutron stars

[vu10758]

Neutron stars represent the final stage of life for some massive stars. Typically, they have radii of 10 km. Determine the magnitude of the centripetal acceleration for a piece of neutron star matter on the star surface at the equator (so the matter moves in a circle of radius 10km). Assume the neutron star rotates once every .003 seconds.

This is what I did.

a = w^2 * r
a = (2pi/.003)^2 * (10)
a = 4.38 x 10^7 m/s^2

The answer key tells me that the acceleration is 4.37 x 10^10 m/s^2. Where did I go wrong?

 

[BishopUser]

remember to convert everything into SI units. You used 10km when you should have used 1000m :p

 

[kyle8921]

It appears that you have made a small error in your calculation. The correct formula for centripetal acceleration is a = (2πf)^2r, where f is the frequency of rotation (in Hz), not the angular velocity (w). So the correct calculation would be:

a = (2π/0.003)^2 * (10)
a = 4.37 x 10^10 m/s^2

This is a very high acceleration, which is expected for objects as dense and compact as neutron stars. It is important to note that this acceleration is only applicable at the equator, as the acceleration decreases towards the poles due to the oblate shape of the neutron star. Additionally, this calculation assumes a perfect, uniform rotation, which may not be the case for all neutron stars. Further studies and observations are needed to fully understand the dynamics of these fascinating objects.