Example: Neutron Star Rotation
A neutron star is the collapsed core of a large star (usually of a red giant). Neutron stars are the smallest and densest stars known to exist, but they are rotating extremely rapidly. This rapid rotation is a direct consequence of the law of conservation of angular momentum. As the star’s core collapses, its rotation rate must increase, because of conservation of angular momentum, hence newly formed neutron stars must rotate at up to several hundred times per second. Some neutron stars emit beams of electromagnetic radiation that make them detectable as pulsars.
Assume a neutron star of a radius of 7 x 105 km, which collapses under its own gravitation to a radius of 10 km. This star is rotating at a frequency of 1.0 revolution every 30 days. Assume that the star is a homogenous sphere at all times, and loses no mass.
From the law of conservation of angular momentum:
I1ω1 = I2ω2
where the subscripts 1 and 2 refer to initial star and neutron star, respectively. The moment of inertia of a sphere about its central axis is:
I = ⅖ m1r12