# 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.

kg-m2
kg
m/s2
m
s ## Formula

Period:
T = 2∏√(I/MgD)

Center of Mass or Moment of Inertia:
I = T2 MgD/4 ∏2

Mass:
M = 4 ∏2I/gDT2

Acceleration of Gravity:
g = 4 ∏2I / MDT2

Distance from Center of Mass to Pivot:
D = 4 ∏2I / Mg T2

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-m2
Mass (M) = 15 kg
Acceleration of Gravity (g) = 10 m/s2
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 