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# Physical Pendulum Calculation

Physical Pendulum consists of an actual object that is allowed to rotate freely around a horizontal axis. A physical pendulum is used to regulate a clockwork mechanism. A pendulum is a mass that is attached to a pivot, from which it can swing freely. Pendulum consisting of an actual object allowed rotating freely around a horizontal axis. This is called Physical Pendulum.

Table of Contents:

## Formula

Period:

**T = 2∏√(I/MgD)**

Center of Mass or Moment of Inertia:

**I = T ^{2} MgD/4 ∏^{2}**

Mass:

**M = 4 ∏ ^{2}I/gDT^{2}**

Acceleration of Gravity:

**g = 4 ∏ ^{2}I / MDT^{2}**

Distance from Center of Mass to Pivot:

**D = 4 ∏ ^{2}I / Mg T^{2}**

**Where,**

T = Period,

I = Center of Mass or Moment of Inertia,

M = Mass,

g = Acceleration of Gravity,

D = Distance from Center of Mass to Pivot.

A physical pendulum consists of a large mass that is suspended from a rod. Its displacement is used to measure the velocity of a projectile. This advanced online Physical Pendulum Calculation tool is used to calculate and find the various parameters of a physical pendulum.

**Example:**

Calculate the time Period taken by a Physical Pendulum to rotate by the given details of the pendulum.

Center of Mass or Moment of Inertia (I) = 25 kg-m^{2}

Mass (M) = 15 kg

Acceleration of Gravity (g) = 10 m/s^{2}

Distance from Center of Mass to Pivot (D) = 5 m

**Solution:**

**Apply Formula:**

T = 2∏√(I/MgD)

T = 2*3.14 √(25/15*10*5)

T = 6.28 √(25/750)

T = 6.28 √0.033

T = 6.28*0.182

T = 1.1429

T = 1.15 s

**Period (T) = 1.15 s**