I’d prefer thorough solutions, but if you can only provide formulas that would solve each part of the problem, that’d be helpful too :-) Thanks!
Spinning too fast
The rate of rotation of astrophysical objects that are held together by gravity (e.g., stars or planets) cannot be larger than a certain maximum. Rotating faster than this rate will tear the star apart. Let’s find the expression for this maximum rotation rate.
a) You are sitting on the equator of a star of radius R that is spinning about its axis with period P. What is the rotation speed that you have on the equator?
b) Using your expression for the rotation speed, what is the centrifugal acceleration that you experience on the equator?
c) The star has mass M. What is the gravitational acceleration that you feel on the surface?
d) Now equate the centrifugal and gravitational acceleration, and find the period of rotation when they are equal. What happens if the star rotates faster than this period?
e) Calculate the limiting rotation periods for the Earth and for the Sun. Write them in the most appropriate units (e.g., seconds, minutes, hours, days, years, etc.). Find the ratio of the critical rotation period for the Earth to the current rotation period. The Sun is rotating with a period of 25 days. Find this ratio for the Sun as well.
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