Glossary
Angular Acceleration (α)
Angular acceleration is the rate at which an object's angular velocity changes, indicating how quickly its rotational speed is increasing or decreasing.
Example:
When a spinning top starts to slow down, it experiences a negative angular acceleration.
Moment of Inertia (I)
Moment of inertia is the rotational equivalent of mass, quantifying an object's resistance to changes in its rotational motion, which depends on both its mass and how that mass is distributed around the axis of rotation.
Example:
An ice skater pulls their arms in to decrease their moment of inertia and spin faster.
Newton's Second Law for Rotation
This fundamental law states that the net torque (∑𝜏) acting on an object is directly proportional to its moment of inertia (I) and its angular acceleration (α), expressed as ∑𝜏 = Iα.
Example:
This law explains why a massive merry-go-round with a large moment of inertia requires a significant net torque to get it spinning quickly.
Perpendicular Component of Force (for Torque)
Only the component of an applied force that acts perpendicularly to the radius vector (the distance from the pivot to the force application point) contributes to creating torque.
Example:
Pushing a door directly into its hinges creates no torque because there is no perpendicular component of force relative to the pivot.
Pivot Point (Axis of Rotation)
The pivot point, also known as the axis of rotation, is the fixed point or line around which an object rotates.
Example:
The hinges of a door act as its pivot point when you open or close it.
Rotational Equilibrium
Rotational equilibrium occurs when the net torque acting on an object is zero, meaning the object is either at rest or rotating at a constant angular velocity.
Example:
A perfectly balanced seesaw, where the torques from children on both sides cancel out, is in rotational equilibrium.
Sign Convention (for Torque)
The sign convention for torque is a standard rule for assigning positive or negative values to torque, typically considering counter-clockwise torque as positive and clockwise torque as negative.
Example:
When setting up equations for a rotating system, you must consistently apply the sign convention to ensure correct calculations of net torque.
Torque
Torque is the rotational equivalent of force, representing the twisting action that causes an object to rotate or change its rotational motion.
Example:
When you use a wrench to tighten a bolt, the twisting force you apply is torque.