Question

A uniform disk with mass M and radius R is rotating about an axis through its center-of-mass. The axis is perpendicular to the disk. The moment of inertial for the disk with a central axis is I MR2. Two non-rotating smaller disks, each with mass M2 and radius R/4, are glued on the original disk as shown in the figure.

 (a) Show that the ratio of the moments of inertia is given by  I'/I = 35/16, where I' is the moment of inertia for rotation about the central axis of the big disk after the smaller disks are added. (Hint: the Parallel-Axis Theorem is useful)  

(b) The disk is initially rotating with o 5.0 rad/s before the smaller disks are added. Find the angular velocity ' of the entire system after the smaller disks, originally non-rotating, are glued. (M-1.3 kg, R-0.8 m)  

Answer 1

2 (a) According to the parallel axis theorem

i.e. New Moment of inertia is the moment of inertia through the center of mass + the mass times the perpendicular distance between the axes of the disk.

New mass

R between the axes of the disk =

(b)  

Since R' = R