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
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 ?