Physical Pendulum Calculator

Enter value and click on calculate. Result will be displayed.
Select calculator :
 
Center of Mass or Moment of Inertia(I) :
kg-m2
Mass (M) :
kg
Acceleration of Gravity(g) :
m/s2
Distance from Center of Mass to Pivot(D) :
m
Result:

A Physical Pendulum Calculator is a tool used to calculate the period of oscillation of a physical (compound) pendulum — an object that swings back and forth around a fixed pivot point, where its mass is distributed along its length (unlike a simple pendulum, which assumes all mass is concentrated at a point).

What is a Physical Pendulum?
A physical pendulum is a rigid body that swings under the influence of gravity, where the mass is not concentrated at one point but spread across the object’s shape and size. Examples include:

  • A swinging rod fixed at one end
  • A door rotating on its hinges
  • A swinging disc or plate

The period of oscillation (T) for a physical pendulum is given by:

Where:

  • T = Period of oscillation (time for one complete swing)
  • I = Moment of inertia of the pendulum around the pivot (kg·m²)
  • m = Mass of the pendulum (kg)
  • g = Acceleration due to gravity (9.81 m/s² on Earth)
  • d = Distance from the pivot point to the pendulum’s center of mass (m)

Why use a Physical Pendulum Calculator?

  • Saves Time: Quickly determines the period without lengthy calculations.
  • Ensures Accuracy: Reduces human error in complex formulas.
  • Engineering Applications: Used in designing mechanical systems involving oscillations.
  • Educational Tool: Helps students understand pendulum motion in physics.

How does a Physical Pendulum Calculator work?

  • Input:
    • Mass of the object (m)
    • Moment of inertia (I)
    • Distance from the pivot to the center of mass (d)
    • Gravitational acceleration (optional — typically 9.81 m/s2)
  • Calculation: Uses the formula for the period of a physical pendulum.
  • Output: Period of oscillation (T), usually in seconds.

When should you use a Physical Pendulum Calculator?

  • In physics experiments: Studying the motion of physical pendulums.
  • For mechanical design: Calculating oscillation periods in machinery.
  • In clock-making: Designing pendulum clocks with accurate timing.
  • For structural analysis: Studying swinging behavior of suspended objects.