Angular momentum
kg·m²/s
Signed axial angular momentum L = Iω.
Physics · Mechanics · Motion & Energy
Angular momentum calculator
Calculate the axial angular momentum of a rigid body from its mass moment of inertia and angular speed, or solve either quantity inversely.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
Results
Mass moment of inertia
Positive mass moment of inertia about the selected axis.
Angular speed
Signed angular velocity about the selected axis.
Relation and numerical substitution
L = I × ω—
Rigid body rotating about a fixed axis with constant positive mass moment of inertia; L and ω use the same sign convention.
01Formulas and symbols
Formulas used
L
L = I × ωAngular momentum for a rigid body rotating about a fixed principal axis.I
I = L / ωMoment of inertia inferred from angular momentum and nonzero angular speed.ω
ω = L / IAngular speed inferred from angular momentum and positive moment of inertia.02Assumptions and limits
Scope of validity
- Rigid body rotating about a fixed axis with constant positive mass moment of inertia; L and ω use the same sign convention.
03Validation example
Reference numerical case
- For I = 0.5 kg·m² and ω = 10 rad/s, L = 0.5 × 10 = 5 kg·m²/s.
- The inverse modes recover I = 0.5 kg·m² and ω = 10 rad/s.
04References
Technical references
FAQ
How is angular momentum different from rotational kinetic energy?
Angular momentum is L = Iω and keeps the sign of angular velocity. Rotational kinetic energy is K = ½Iω² and is nonnegative, so the two quantities describe different aspects of the same rotation.
Why convert rpm to rad/s?
The relation L = Iω in SI uses angular velocity in radians per second. The unit selector converts revolutions per minute to rad/s before the calculation, while preserving the physical rotation rate.
05How it works
For a fixed axis, increasing either I or |ω| increases |L| proportionally. Reversing the direction of rotation changes the sign of ω and L but does not change I.
06Limits of the model
The scalar relation L = Iω applies directly to rigid-body rotation about a fixed principal axis. General three-dimensional rigid-body motion can require vector angular momentum that is not parallel to angular velocity.
07Common mistakes
Use a mass moment of inertia in kg·m², not a geometric second moment of area in m⁴. Do not enter rpm as if it were rad/s.