Physical Pendulum Period
Period of a rigid body oscillating about a pivot point (physical/compound pendulum).
Variables
Derivation
Torque τ = -mgd·sin(θ) ≈ -mgdθ for small angles. Using τ = Iα: Iα = -mgdθ, giving ω² = mgd/I and T = 2π√(I/mgd).
Your notes
Constants in this formula
Check value
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- I = 2 kg·m² (Moment of inertia)
- m = 3 kg (Mass)
- g = 9.806 65 m/s² (Gravitational acceleration)
- d = 4 m (Distance to center of mass)
Result: T = 0.81911316 s
Other waves formulas with the same quantities
- Spring Oscillation Period (Simple Harmonic Motion) shares Period, Mass
- Torsional Oscillation Period (Simple Harmonic Motion) shares Period, Moment of inertia
- SHM Total Energy (Simple Harmonic Motion) shares Mass
- Damped Oscillation (Simple Harmonic Motion) shares Mass
- Quality Factor (Q Factor) (Simple Harmonic Motion) shares Mass
- Period and Frequency (Wave Properties) shares Period
Where this formula is listed
- Waves formulas, under Simple Harmonic Motion, alongside SHM Displacement, SHM Velocity, SHM Acceleration, SHM Maximum Velocity and Resonance Amplitude.
- In the waves list it comes after SHM Total Energy and before Torsional Oscillation Period.
- Waves formula sheet, one of 37 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
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)).