Glossary
Angular Momentum
A measure of an object's tendency to continue rotating, analogous to linear momentum for translational motion. It is calculated as the product of an object's moment of inertia and its angular velocity.
Example:
A spinning top possesses significant angular momentum, allowing it to remain upright and stable.
Angular Velocity
The rate at which an object rotates or revolves around an axis, typically measured in radians per second. It describes how fast something is spinning.
Example:
A record player spins at a constant angular velocity of 33 1/3 revolutions per minute, ensuring the music plays at the correct speed.
Central Force
A force that always points directly towards or away from a fixed point or center. In orbital mechanics, gravitational force is a central force, which leads to the conservation of angular momentum.
Example:
The gravitational pull of the Earth on a satellite is a central force, always directed towards the Earth's center, keeping the satellite in orbit.
Conservation of Angular Momentum
A fundamental principle stating that the total angular momentum of a system remains constant if no net external torque acts on it. This means angular momentum is neither gained nor lost within the isolated system.
Example:
When a diver tucks their body mid-air, their conservation of angular momentum causes them to spin faster as their moment of inertia decreases.
Inelastic Collision
A type of collision where kinetic energy is not conserved, although momentum (linear or angular) may still be conserved. Some kinetic energy is typically converted into other forms, such as heat, sound, or deformation.
Example:
When a piece of clay is dropped onto a spinning disk and sticks, it's an inelastic collision because kinetic energy is lost as the clay deforms and heats up.
Kepler's 2nd Law
States that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This law is a direct consequence of the conservation of angular momentum for orbiting bodies.
Example:
Earth moves faster when it's closer to the Sun, demonstrating Kepler's 2nd Law by sweeping out the same area in a given time as when it's farther away and moving slower.
Moment of Inertia
A measure of an object's resistance to changes in its rotational motion, depending on its mass distribution relative to the axis of rotation. The farther the mass is from the axis, the greater the moment of inertia.
Example:
It's much harder to spin a long, heavy pole around its end (high moment of inertia) than around its center, where the mass is more evenly distributed.
Torque
A twisting force that causes or changes rotational motion. It is the rotational equivalent of linear force and is required to change an object's angular momentum.
Example:
Applying a wrench to a stubborn bolt requires sufficient torque to loosen it, causing it to rotate.