Pulsars are neutron stars that emit X rays and other radiation in such a way tha

Question

Pulsars are neutron stars that emit X rays and other radiation in such a way that we on Earth receive pulses of radiation from the pulsars at regular intervals equal to the period that they rotate. Some of these pulsars rotate with periods as short as 1 ms! The Crab Pulsar, located inside the Crab Nebula in the constellation Orion, has a period currently of length 33.085 ms. It is estimated to have an equatorial radius of 15 km, an average radius for a neutron star. (a) What is the value of the centripetal acceleration of an object on the surface at the equator of the pulsar? 5.4e8 m/s (b) Many pulsars are observed to have periods that lengthen slightly with time, a phenomenon called "spin down." The rate of slowing of the Crab Pulsar is 3.50 × 10-13 s per second, which implies that if this rate remains constant, the Crab Pulsar will stop spinning in 9.50 × 1010 s (about 3000 years from today). what is the tangential acceleration of an object on the equator of this neutron star? 3e-5 X m/s2 The circular path that the object at the equator undergoes has a radius equal to that of the star, and therefore is simply the equatorial circumference-and is traversed in a time interval of one period. eBook

Explanation / Answer

Since the rate of period change, not rotation rate change, is given, the rotational and tangential acceleration depend on the current rotation rate. From the rate of period change dT/dt, the current period T and the radius r, calculate the tangential acceleration:
Rot. rate = 2pi/T rad/s
Rot. acc. = - 2pi/(T+3.5E-13) rad/s^2
Tang. acc. = r m/s^2
EDIT (response to evalesco): OK, I was a little careless so the units seem inconsistent. T+3.5E-13 s is the period 1 s after T is measured, to conform with the given rate of change of the period. I should have written
Rot. acc. = ( - 2pi/(T+3.5E-13))/t where t = 1s. Then the unit rad/s^2 makes sense and we have
1 = 2pi/0.033085 = 189.910391633054 rad/s
2 = 2pi/(T+3.5E-13) = 2pi/0.03308500000035 = 189.910391631045 rad/s
Rot. acc. = (-2)/1 = 2.009E-9 rad/s^2
Tang. acc. = 2.009E-9*15000 = 3.0135E-5 m/s^2

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