Consider the simple pendulum shown on page 1 of the lab manual:a ball hanging at

Question

Consider the simple pendulum shown on page 1 of the lab manual:a ball hanging at the end of a string. Derive the expression forthe period of this physical pendulum, taking into account thefinite size of the ball (i.e. the ball is not a point mass). Assumethat the string is massless. Start with the expression for theperiod T of a physical pendulum with small amplitudeoscillations:



Here I is the moment of inertia about an axis through the pivot(fixed point at the top of the string), m is the mass of the ball,g is the Earth's gravitational constant of acceleration, and h isthe distance from the pivot at the top of the string to the centerof mass of the ball. The moment of inertia of the ball about anaxis through the center of the ball is



b. Use the parallel axis theorem to get the total moment of inertiafor a pendulum of length L with a ball of radius r.

Explanation / Answer

T = 2 ( I / mgL)

I = 2/5 m r^2

T = 2 [ (2/5) r² /gL)

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