Glossary
Angular acceleration
The rate of change of angular velocity, indicating how quickly an object's rotational speed or direction is changing.
Example:
As a merry-go-round speeds up from rest, it experiences a positive angular acceleration.
Angular frequency
A measure of how quickly an object oscillates or rotates, defined as $2\pi$ times the frequency or $2\pi$ divided by the period.
Example:
A speaker cone vibrating rapidly has a high angular frequency, producing a high-pitched sound.
Energy Conservation
A fundamental principle stating that the total mechanical energy (sum of kinetic and potential energy) of a system remains constant if only conservative forces are doing work.
Example:
A roller coaster car speeding down a hill and then climbing another hill demonstrates Energy Conservation, converting potential energy to kinetic energy and back.
Moment of inertia
A measure of an object's resistance to changes in its rotational motion, depending on its mass and how that mass is distributed relative to the axis of rotation.
Example:
A figure skater pulls their arms in to decrease their moment of inertia, allowing them to spin faster.
Newton's Second Law (Rotational Form)
States that the net torque acting on a rigid body is equal to the product of its moment of inertia and its angular acceleration ($ au = I\alpha$).
Example:
When a mechanic uses a wrench to tighten a bolt, the applied torque causes the bolt to undergo Newton's Second Law (Rotational Form), resulting in angular acceleration.
Period (of a physical pendulum)
The time it takes for a physical pendulum to complete one full oscillation, given by the formula $T_{ ext{phys}} = 2\pi \sqrt{\frac{I}{mgd}}$.
Example:
If a grandfather clock's pendulum takes 2 seconds to swing back and forth, its period is 2 seconds.
Physical pendulum
A real-world object with a complex shape and distributed mass that swings around a fixed pivot point, where its motion depends on its mass distribution.
Example:
A swinging meter stick pivoted at one end is an example of a physical pendulum, where its distributed mass affects its oscillation period.
Rigid object
An object whose shape and size do not change during its motion, meaning the distance between any two points within the object remains constant.
Example:
A spinning top can be considered a rigid object because its form does not deform as it rotates.
Simple Harmonic Motion (SHM)
A type of periodic motion where the restoring force is directly proportional to the displacement and acts in the opposite direction, resulting in sinusoidal oscillations.
Example:
A mass oscillating on a spring, when stretched and released, exhibits Simple Harmonic Motion.
Simple pendulum
An idealized model consisting of a point mass attached to a massless string, used as a simplified case for oscillatory motion.
Example:
A small, heavy ball suspended by a very light thread, swinging with minimal air resistance, approximates a simple pendulum.
Small angle approximation
A mathematical simplification where, for small angles (in radians), $\sin heta \approx heta$, used to linearize oscillatory equations and simplify calculations.
Example:
When analyzing the swing of a playground swing, using the small angle approximation simplifies the math to predict its period accurately for small displacements.
Torque
A rotational force that tends to cause an object to rotate about an axis, calculated as the product of force and the perpendicular distance from the pivot to the line of action of the force.
Example:
Applying a force to the end of a lever creates torque, causing it to rotate around its fulcrum.