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Waves
Waves

Physical Pendulum Period

T=2πImgdT = 2\pi\sqrt{\frac{I}{mgd}}

Period of a rigid body oscillating about a pivot point (physical/compound pendulum).

Variables

T
Period
Time for one oscillation
s
I
Moment of inertia
About pivot point
kg·m²
m
Mass
Total mass of pendulum
kg
g
Gravitational acceleration
≈ 9.8 m/s²
m/s²
d
Distance to center of mass
From pivot to CM
m

Derivation

Torque τ = -mgd·sin(θ) ≈ -mgdθ for small angles. Using τ = Iα: Iα = -mgdθ, giving ω² = mgd/I and T = 2π√(I/mgd).

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Common questions

What is the Physical Pendulum Period formula?

Physical Pendulum Period is written T = 2π√(I/mgd). Period of a rigid body oscillating about a pivot point (physical/compound pendulum). It belongs to Waves, under Simple Harmonic Motion.

What are the units in T = 2π√(I/mgd)?

In SI units, T is period, measured in s; I is moment of inertia, measured in kg·m²; m is mass, measured in kg; g is gravitational acceleration, measured in m/s²; d is distance to center of mass, measured in m.

How is the Physical Pendulum Period formula derived?

Torque τ = -mgd·sin(θ) ≈ -mgdθ for small angles. Using τ = Iα: Iα = -mgdθ, giving ω² = mgd/I and T = 2π√(I/mgd). The result is T = 2π√(I/mgd).