角动量

Angular momentum is the product of moment of inertia and angular velocity of a rotating object. For a ball on a string, angular momentum L equals the radius times translational momentum. Since momentum is mass times velocity, and tangential velocity equals angular velocity times radius, angular momentum depends on both the object's mass distribution and rotational speed.

Curl the fingers of your right hand in the direction of rotation. Your extended thumb points in the direction of the angular momentum vector. This rule applies to all rotating systems and helps visualize whether angular momenta add or cancel when multiple objects rotate together.

When a skater pulls their arms inward, the radius decreases, reducing moment of inertia. By conservation of angular momentum, if radius decreases and no external torque acts, angular velocity must increase to keep angular momentum constant. This is why the skater rotates significantly faster with arms pulled close to the body.

Flipping the wheel reverses its angular momentum direction. Since the system has no external torque, total angular momentum must remain conserved. The person and chair spin in response, generating angular momentum that opposes the wheel's new direction, keeping the system's total angular momentum unchanged.

Torque equals tension in the string times the radius of the axle. This torque causes rotational acceleration of the rod. Angular acceleration equals torque divided by moment of inertia. Using rotational kinematics, you can calculate angular velocity and then determine angular momentum at any time during the rod's rotation.

Moving bicycle wheels possess angular momentum perpendicular to the frame. Larger angular momentum requires greater torque to change direction, making the bike harder to tip over. This rotational stability from the wheels' angular momentum is why cyclists naturally balance better at speed.

Helicopters have two rotors spinning in opposite directions, creating opposing angular momenta. These angular momenta cancel each other out, conserving total angular momentum for the entire system. This balance prevents the helicopter body from spinning uncontrollably in response to rotor motion.