# Period of small oscillation of sphere rolling in cylinder

A solid sphere is rolling without slipping on a vertical circular ramp with radius R. The sphere has radius r and mass m with a moment of inertia I = (2/5)m r^2. Find the period of a small amplitude oscillation.

(See attached file for full problem description with diagram and equations)

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#### Solution Preview

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A solid sphere is rolling without slipping on a vertical circular ramp with radius R. The sphere has radius r and mass m with a moment of inertia I = (2/5)mr^2. Find the period of a small amplitude oscillation.

hints:

force method- relate alpha with tangential acceleration and then relate them to the second derivative of theta with respect to time (alpha does not equal the ...

#### Solution Summary

A sphere rolls without slipping on a cylindrical ramp. Period of small oscillations calculated.