Expert: Philip A. Stahl - 9/5/2008

Question
QUESTION: I recently sent you a question about a rotating pulsar.  The whole question is: The Crab Pulsar, located inside the Crab Nebula in the constellation Orion, has a period currently of length 33.085ms.  It is estimated to have and equatorial radius of 15km.  (a)What is the value of the centripetal acceleration of an object on the surface at the equator of the pulsar?  (b)The rate of slowing of the Crab Pulsar is 3.5x10^-13s per second so the pulsar will stop spinning in 9.5x10^10s. What is the tangential acceleration of an object on the equator of this neutron star?

ANSWER: Okay, the only things we need to know relevant to the question you asked is: the radius, and the time for rotation. A period of about 33 ms means that it makes about 30 rotations per second, so call the time t = 1/30 s.

The radius of 15 km translates to 15000 m = 1.5 x 10^4 m

The rotational velocity is then:

v(r) ~   2 pi(r)/ t  =  9.4 x 10^4 m/  (1/30s)

v(r) =  2.8 x 10^6 m/s

So, its rotational velocity is way under light speed (3 x 10^8 m/s) , by nearly a factor 100.

I suspect somehow you used the wrong units or made an incorrect conversion.

Hope this helps!

---------- FOLLOW-UP ----------

QUESTION: Thanks.  I reworked the problem before you responded and got that answer as well.  However, it later asked for the centripetal acceleration A=V^2/r.  I used the acceleration found earlier, 2.8x10^6 m/s, and got 5.4x10^8 m/s. Is this possible?

Answer
Actually, that value is:

5.3 x 10^8 m/s^2

Not m/s!

Remember this is an acceleration, and actually a centripetal acceleration - so yes, it is feasible.

As you will recall (or google!) centripetal acceleration is defined mostly on the basis of *change in direction of the vector v* not magnitude! Hence, the plausibiliy of the answer.

To remind you of the pertinent points, you can go here:

http://dev.physicslab.org/Document.aspx?doctype=3&filename=CircularMotion_Centri


Note the acceleration in question results largely from the *direction change* of (v_f - v_o)

Hope this helps!