Foundational Physics

Short Answer: Angular momentum stays constant when the net external torque on a system is zero. Forces within the system can change how its parts rotate, but they exchange angular momentum rather than create or destroy the total. A torque from outside the system is needed to change that total.

How Can Two People Change Their Spins Without Changing the Total?

Imagine two people sitting on a freely rotating platform with very little friction. At first, they and the platform are at rest. The people push tangentially against one another, so each feels a twisting effect in an opposite direction.

One person may begin rotating one way while the other rotates the opposite way. If the platform also moves, its angular momentum must be included. The motion of each part can change, yet the angular momenta of all the parts together still add to the original total—zero in this example.

The two people have not pulled angular momentum from nowhere. They have exchanged it through their interaction.

Why Do Internal Torques Cancel?

When one person pushes on the other, the other pushes back with an equal and opposite force. The interaction can give one part angular momentum in one direction and another part angular momentum in the other direction.

About the same reference point, the torques the two people exert on one another are equal and opposite, so they do not change the total angular momentum of the two-person system. In a real setup, include the platform if forces from it transfer angular momentum between the people and the platform.

Internal interactions rearrange angular momentum; they do not change the combined total. That conclusion assumes we count all interacting parts and use a single consistent reference point.

What Does an External Torque Change?

Now imagine that someone standing on the floor grabs the platform’s rim and twists it. That person is outside the chosen people-plus-platform system. The applied external torque can change the system’s total angular momentum.

A bearing with friction can also exert an external torque that gradually reduces the rotation. That is why a real platform eventually slows down, even though an ideal isolated platform would keep its total angular momentum constant.

Is Conservation the Same as Constant Speed?

No. Conservation applies to total angular momentum, not necessarily to the angular speed of each person or object. Parts of a system can redistribute mass and exchange angular momentum with one another.

For example, a skater pulling their arms inward can spin faster while keeping approximately the same angular momentum. That is the application explained in our separate article on why pulling your arms in makes you spin faster. The general reason angular momentum is conserved is the absence of net external torque.

Is There an Even Deeper Reason?

There is. At a deeper level, angular momentum conservation is connected to rotational symmetry: the laws of physics do not depend on which direction we choose to face. This connection is described by Noether’s theorem.

For an introductory physics question, the practical rule is enough: the change in a system’s angular momentum is set by the net external torque acting over time.

The Key Idea to Remember

Angular momentum is conserved for a system when its net external torque is zero. Internal forces and torques can redistribute angular momentum among its parts, but cannot change the total. External torque is what changes that total.

When This Breaks

The conclusion does not apply unchanged if the chosen system experiences a nonzero net external torque. Friction at an axle, a hand twisting the platform from outside, or an external contact force can alter its angular momentum.

Also, angular momentum is defined about a chosen point or axis. Switching reference points or leaving out a moving platform can make an otherwise correct conservation argument seem contradictory. Keep the system and reference point consistent.

Keep Exploring

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