Created By : Vaibhavi Kumari

Reviewed By : Phani Ponnapalli

Last Updated : May 17, 2023

Physical Pendulum Calculator is an online tool that uses inputs to calculate the frequency and period of a physical pendulum. Use this time-saving tool to expedite your computations and get the time period and frequency in no time.

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

What Does the Physical Pendulum Mean?

In physics, a simple pendulum is described as a point mass suspended from fixed support by a light inextensible string. The mean position of the simple pendulum is represented by a vertical line passing through the fixed support. A compound pendulum is a swinging rigid body that is free to rotate around a fixed horizontal axis.

The distance from the pivot to the centre of oscillation is the appropriate equivalent length (L) for determining the period of any such pendulum. This point is placed beneath the pendulum's centre of mass, at a distance from the pivot known as the radius of oscillation, which is determined by the pendulum's mass distribution. The formula for calculating the time period (T) of a physical pendulum is T = 2π × √(I/MgD)

  • Here, I = Moment of inertia
  • M = Mass
  • g = Acceleration due to gravity
  • D = Distance from the centre of mass to pivot.

Moment of Inertia

The period of oscillations is determined by the mass and moment of inertia of the item. The moment of inertia describes how the object's mass is dispersed. Different moments of inertia can be found in objects of the same shape and weight. For example, suppose the mass is evenly distributed in one and concentrated in only a few regions in the other. The reference point determines the moment of inertia.

Oscillation Radius of a Simple Pendulum

Consider a pendulum with mass m that is suspended from the end of a rope with length l. The pivot point is located on the opposite end of the rope. The mass will be centred on the ball and even have a centre of mass if the rope is very light. R = l is the length from the pivot point to the centre of mass, and m x I^2 is the moment of inertia.

The length of the rope is equal to the radius of the oscillations. We can find the time period of oscillations in a basic pendulum by combining all of them. T = 2π x √(l / g)

Physical Pendulum Examples

Question 1:If the moment of inertia is 50 kg*m2, the mass is 6.4 kg, and the distance from the centre of mass to the pivot is 7.4 m, how long does it take the Physical Pendulum to rotate?


Given: Moment of Inertia I = 50 kg*m²

Mass m = 6.4 kg

Acceleration due to gravity g = 9.8 m/s²

Center of Mass to Pivot R = 7.4 m

Time Period T = 2π x √(I / (g x m x R))

T = 2π x √(50 / (9.8 x 6.4 x 7.4))

T = 2.0622 Sec

FAQs on Physical Pendulum Calculator

1. What is a physical pendulum?

The physical pendulum is defined as a rigid body that is suspended on a horizontal axis through its centre of suspension and vibrates freely around its equilibrium position when it is displaced, as opposed to a simple pendulum.

2. How do you determine a pendulum's period?

The period of each full oscillation is constant. T = 2π x √(l / g), where L is the length of the pendulum and g is the acceleration due to gravity, is the formula for the period T of a pendulum.

3. What's the difference between a physical and a simple pendulum?

The centre of the pendulum bob is affected by gravity in the simple pendulum. The force of gravity acts on an object's centre of mass (CM) in the case of a physical pendulum. The item revolves around point O.

4. What are some physical pendulum examples?

A baseball bat swinging back and forth is an example of a physical pendulum. A physical pendulum can experience simple harmonic motion in the same manner that a simple pendulum can under specific conditions.

5. What factors should be taken into account while describing the motion of a physical pendulum?

The object's mass, gravity, and rotational axis. Instead of a point mass, a rigid body is turned to oscillate in this scenario, as indicated in the diagram. There isn't any string requirement.