Physical Pendulum

When we can make any object oscillate like a pendulum it is called a Physical pendulum. Any object hanging at a fixed point if given a force can oscillate like a pendulum and the equations of the pendulum are satisfied by these objects (with slight changes). The motion of this hanging object is considered to be an SHM motion. 

Any object whose motion is similar to the simple pendulum is called a Physical pendulum.

The physical pendulum is shown in the image given below,

Period of a Physical Pendulum

The period of the physical pendulum is the time taken by it to complete one revolution it can be calculated using the angular frequency of the physical pendulum.

The period of a physical pendulum can be calculated using the formula,

T = 2π√(I/mgd)

where,
T is the period of the pendulum 
I is the moment of inertia of the pendulum
m is the mass of the pendulum 
g is the acceleration due to gravity 
d is the distance between the pivot point and the centre of mass 

Equation for Physical Pendulum

Newton’s second law gives the equation of the physical pendulum. For an object of mass m and displacement of the centre of gravity of the pendulum are d and the angular displacement of the physical pendulum is θ then its torque is given by the formula,

τ = -mgd sinθ

here, g is the gravity of the Earth and its value is 9.8m/s²

Example of Physical Pendulum

Various examples which can be considered as the physical pendulum includes,

• A rod hanging on the nail.
• An umbrella hanging from the hook
• A hanging bell, etc.

Check: Oscillation

A rigid body that is capable of rotating around an axis makes up a physical pendulum, a particular kind of pendulum. The physical pendulum can be shaped into a straight rod, a rectangular plate, or a circular disc, in contrast to a basic pendulum, which consists of a tiny mass hanging by a string. The moment of inertia, the separation between the pivot point and the center of mass, and the gravitational pull all affect how a physical pendulum swings.