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nissanztt90
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Homework Statement
Write out expressions for the rotational speed (at the equator) and rotational period of an object mass M and radius R that is spinning at the break up velocity.
Homework Equations
[tex]F= mg[/tex]
[tex]F = m \omega^2 r[/tex]
[tex]g = \frac{mG}{r^2}[/tex]
The Attempt at a Solution
So i know that for something to be "flung" off the spining mass, the centrifugal acceleration would need to be greater than the gravitational acceleration.
So i just set them equal to each other, and solve for omega...
which is...
[tex]\sqrt{\frac{mg}{r^3}} < \omega[/tex]
And for the rotation period...
[tex]p < \frac{2\pi}{\sqrt{\frac{mG}{r^3}}} [/tex]
Is this correct?
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