A uniform flat disk of radius R and mass 2M is pivoted at point P. A point mass

Question

A uniform flat disk of radius R and mass 2M is pivoted at point P. A point mass of 1/2 M is attached to the edge of the disk. Calculate the moment of inertia I_CM of the disk (without the point mass) with respect to the central axis of the disk, in terms of M and R. Calculate the total moment of inertia I_p of the disk (with the point mass) with respect to point P, in terms of M and R. Calculate the total moment of inertia I_T of the disk with the point mass with respect to point P, in terms of M and R.

Explanation / Answer

(A) Icm = m r^2 / 2

= (2 M) (R^2) / 2 = M R^2

(b) Applying parallel axis thereom,

Ip = Icm + m d^2

Ip = ( M R^2) + (2 M) (R^2)

Ip = 3 M R^2

(c) I_T = (3 M R^2) + (M/2) (2R)^2

= 5 M R^2

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