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## Homework Statement

A uniform disc radius a, mass m

there is rotation about an axis (z) tangental to the disc and in the plane of the disc.

a point mass m is placed at the centre of the disc.

what is the new moment about the axis z

also show that the period of oscillations will decrease by SQRT(9/10) when the point mass is added

## The Attempt at a Solution

moment of inertia of just the disc i found to be =

**(5/4)ma^2**

period before point mass added =

T=2pi/w = 2pi*sqrt(m/k)

torque = r x F = mga sin(theta) but we are told small angle approx applies so = mga*theta

also F=k*theta

so k = mga

therefore T = 2pi*sqrt(m/mga) anf because of rotation the m on top = I about z axis

so T = 2pi*sqrt(I/mga) = 2pi*sqrt(5a/4g)

I dont know how to get the I when point mass has been added.

also is the new torque = 2mga * theta so that k = 2mga ?

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