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? (b) Many pulsars are observed to have periods that lengthen slightly with time, a phenomenon called

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. a = ? - 2pi/(T+3.5E-13) rad/s^2

Tang. acc. = ar 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. a = (? - 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. a = (?-?2)/1 = 2.009E-9 rad/s^2

Tang. acc. = 2.009E-9*15000 = 3.0135E-5 m/s^2

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