Created By : Naaz Fatima

Reviewed By : Rajashekhar Valipishetty

Last Updated : Apr 10, 2023

Physical Pendulum Calculator is an online tool that displays the frequency, time period given the related inputs in the calculator tool. Make your computations faster using the handy tool over here and get the time period, frequency in no time.

Choose a Calculation:
Moment of Inertia (I)
Mass (m)
Distance (R)

Physical Pendulum Definition

A Physical Pendulum is an object that performs small oscillations around its equilibrium position. Examples of Physical Pendulum is swing in playgrounds, swinging weight of a pendulum clock, etc. If the Maximum Angle doesn't exceed 15┬║ then the oscillations are small. If the angle exceeds that limit the computations are a bit complicated.

Period of Physical Pendulum

Period of Physical Pendulum can be determined using the formula Period T = 2π * √(I / (g * m * R))

Where I is the moment of inertia and its units are kg*m┬▓

g is the acceleration due to gravity and its units are m/s┬▓

m is the mass of the object and its units are kg

R is the distance from center of mass to pivot point and its units are m

Moment of Inertia can be found depending on the pivot. Acceleration due to gravity on earth's surface is g = 9.81 m/s┬▓

Combination L = I / (m * R) that comes in the period of a physical pendulum is called radius of oscillations. If two different pendulums have same radius of oscillations then they have the same period.


Calculate the time priod taken by the Physical Pendulum to rotate if the moment of inertia is 30 kg*m┬▓, mass is 6 kg, distance from center of mass to pivot is 7 m?


Given that

Moment of Inertia I = 30 kg*m┬▓

Mass m = 6kg

Acceleration due to gravity g = 9.8 m/s┬▓

Center of Mass to Pivot R = 7 m

We know the formula to calculate Time Period T = 2π * √(I / (g * m * R))

Substituting the input values we get the Time Period as T = 2π * √(30 / (9.8 * 6 * 7))

On simplifying further we get the value of T = 1.6954 Sec

Moment of Inertia

Period of Oscillations depend on the moment of inertia and mass of the object. Moment of Inertia tells how mass is distributed in the object. Objects having same shape and weight will have different moment of inertia.

Radius of Oscillations of a Simple Pendulum

Let us consider a pendulum made of mass m and hanged on the end of the rope of length l. Pivot point is on the other end of the rope. If the cord is very light then the mass will be concentrated on the ball and even has center of mass in it. Length is calculated from the pivot point to the center of mass i.e. R = l and moment of inertia is given by m * l┬▓. Radius of oscillations L is equal to rope length. Using all these we can find the time period of oscillations in a simple pendulum as follows

T = 2π * √(l / g)

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FAQs on Physical Pendulum Calculator

1. How to find the Period of a Physical Pendulum?

The Priod of a Physical Pendulum can be found by the formula T = 2π * √(I / (g * m * R))

2. What is meant by Physical Pendulum?

Physical Pendulum is an object that performs small oscillations around its eqilibrium position.

3. What does Period of Pendulum depend on?

The Period of Pendulum depends on the length of the string.

4. What are Examples of a Physical Pendulum?

Examples of Physical Pendulum is a baseball bat swinging back and forth, swing in playgrounds, swinging weight of a pendulum clock.