(a) The angular rotation rate, Ω, at which spacetime is dragged around a rotating mass must be proportional to its angular momentum L. The expression for Ω must also contain the constants G and c, together with the radial coordinate r. Show on purely dimensional grounds that
Ω=constant×r3c2GL,
where the constant (which you need not determine) is of order unity.
(b) Evaluate this for Earth, assuming that it is a uniformly rotating sphere. Set the leading constant equal to one, and express your answer in arcseconds per year. How much time would it take for a pendulum at the north pole to rotate once relative to the distant stars because of frame dragging?
(c) Repeat part (b) for the fastest known pulsar, expressing Ω in revolutions per second.