Pendulum with a Large Bob

Consider the small oscillations of a pendulum having a spherical bob of radius (R) and having a mass (M) as depicted in figure 5.

Figure 5. Pendulum with Large Bob

It is assumed that the bob moves such that the radius PQ continually lies on the line PO that joins the bob center to the point of suspension. The moment of inertia of the sphere considered about the axis parallel to a diameter and 1 cm. away from it will, from the theorem of parallel axes be,

The equation of rotational motion assuming viscous forces are again ignored and the oscillations are small will be.

Hence the period of oscillation will be,

There are many more second order effects that need to be taken into account if the pendulum system is to be used to provide a very accurate measure of the acceleration due to gravity (g). Nevertheless, the pendulum method is one of those most used for this purpose.