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February 27, 2015

February 27, 2015

Posted by **kendell** on Sunday, January 9, 2011 at 4:29pm.

Please help i have no idea how to do this problem

- physics -
**drwls**, Sunday, January 9, 2011 at 7:23pmThink of this as a torsional spring, with a torsional stiffness coefficient

k = (0.37/0.93) = 0.398 N*m/radian

The equation of motion is

I*x" = -kx,

where x is the angular deflection in radians and I is the moment of inertia of the sphere. x" is the second derivative of x, which is the angular acceleration.

The solution to this differential equation leads to a period

P = 2 pi sqrt(I/k)

Look up and compute the moment of inertia of a sphere rotating about its axis. I think you will find that

I = (2/5)M R^2

Solve for period, P. The units will be Hz if I is in kg*m^2

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