Determine the period of small oscillations of the semicylinder of mass m and radius r as

Problem 8.88

Determine the period of small oscillations of the semi-cylinder of mass m and radius r as it rolls without slipping on the horizontal surface.

                                                         Step by Step Solution

Step 1 of 4

Given data:

- The mass of the semi-cylinder is m.

- The radius of the semi-cylinder is r.

The moment of inertia about point O can given as,

Also, the moment of inertia of the semi-cylinder about point O can be given as,

Now, equate the equation (1) and equation (2).