π Angular Momentum Calculator
Calculate L = I Γ Ο for rotating systems.
Result
How to Use This Calculator
This calculator finds angular momentum from moment of inertia and angular velocity. Enter your two values and the result appears instantly in kg m^2/s.
Enter the moment of inertia I in kg m^2. This measures how the object's mass is distributed around its axis of rotation.
Enter the angular velocity in radians per second. If you have revolutions per minute, convert first: multiply rpm by 0.1047 to get rad/s.
Click Calculate, or just keep typing. The result updates automatically as you change the inputs.
Read the angular momentum L in kg m^2/s. Use Clear to reset both fields and start over.
The Angular Momentum Formula
Angular momentum combines how hard an object is to spin (moment of inertia) with how fast it is spinning (angular velocity). A heavy flywheel turning slowly can carry the same angular momentum as a light disk spinning fast, because what matters is the product of the two.
The deeper idea is conservation of angular momentum. When no net external torque acts on a system, its total angular momentum cannot change. That is why a spinning figure skater speeds up dramatically when pulling their arms in: the moment of inertia drops, so the angular velocity rises to keep the product constant. The same principle explains why a collapsing star core spins up into a rapidly rotating neutron star, and why a cat can twist in midair to land on its feet.
Worked Example
Where This Comes Up
You meet angular momentum in physics homework first, usually right after torque. But it shows up in real engineering too. Flywheels in buses and race cars store energy as angular momentum and smooth out power delivery. Gyroscopes in phones and drones use it to sense rotation. Satellite reaction wheels spin one way so the satellite turns the other way, steering spacecraft without thrusters.
A common mistake is mixing up units. Angular velocity must be in radians per second, not degrees per second or rpm. If your answer looks about 60 times too small, you probably entered rpm. Another trap: moment of inertia depends on the axis. The same rod has I = (1/12)ML^2 about its center but (1/3)ML^2 about its end, so always check which axis your problem uses.
Frequently Asked Questions
What is angular momentum?
It is the rotational equivalent of linear momentum. For an object spinning about a fixed axis, angular momentum L equals moment of inertia times angular velocity: L = I x w.
What units does angular momentum use?
Kilogram square meters per second (kg m^2/s). You will sometimes see it written as joule-seconds, which is dimensionally the same.
Why does a figure skater spin faster when pulling in their arms?
Pulling the arms in reduces the skater's moment of inertia. With no external torque acting, angular momentum is conserved, so the angular velocity must increase to keep L = I x w constant.
Is angular momentum always conserved?
Only when the net external torque on the system is zero. Friction at the axle or air resistance applies torque and slowly reduces angular momentum.
What is the difference between torque and angular momentum?
Torque is what changes angular momentum, the same way force changes linear momentum. The relation is torque = dL/dt: torque equals the rate of change of angular momentum.