Pulsars are rotating stars made almost entirely of neutrons packed together. The

Question

Pulsars are rotating stars made almost entirely of neutrons packed together. The rate of rotation of most pulsars gradually decreases because rotational kinetic energy is gradually converted into other forms of energy by a variety of complicated frictional processes. Suppose that a pulsar of mass 1.50 x 10^30 kg and radius 20.0 km is spinning at the rate of 2.10 rev/s and is slowing down at the rate of 1.1 x 10^-15 rev/s2. Treat the pulsar as a sphere of uniform density.

(a) What is the rate (in joules/sec. or watts) at which the rotational energy is decreasing?

(b) If this rate of decrease of the energy remains constant, how long will it take the pulsar to come to a stop? (years)

Explanation / Answer

Kinetic energy,
E = 0.5 * I * w^2
dE / dt = I * w *

At the instant given
I = 2/5 m * R^2 for a sphere
= 2 * 2.1 rad/s
= -2 * 1.1 * 10^-15 rad/s^2

then by putting the values

E = 0.5 * (2/5) * 1.5 * 10^30 * 20000^2 * ( 2 * 3.14 * 2.1)^2

E = 2.087 * 10^40 J

then

dE /dt = ( 2/5) * 1.5 * 10^30 * 20000^2 * 2 * 3.14 * 2.1 * -2 * 3.14 * 1.1 * 10^-15

dE /dt = - 2.18 * 10^25 J/s

then

T = E / (dE/dt)

T = (2.087 * 10^40) / (2.18 * 10^25 ) = 9.5 * 10^14 sec

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