Glossary
Angular Acceleration ($\alpha$)
The rate of change of an object's angular velocity, indicating how quickly its spinning speed is changing.
Example:
A merry-go-round speeding up its rotation experiences angular acceleration.
Angular Displacement ($\Delta heta$)
The angle through which an object rotates about an axis, measured in radians.
Example:
A door opening 90 degrees has an angular displacement of radians.
Angular Velocity ($\omega$)
The rate at which an object rotates or spins, measured in radians per second.
Example:
The angular velocity of a fan blade tells you how fast it's spinning.
Kinetic Friction (in slipping)
A force that opposes the relative motion between two surfaces that are sliding past each other, leading to energy dissipation.
Example:
When you slide a heavy box across the floor, kinetic friction acts against its motion, making it harder to push.
Linear Acceleration ($a_{cm}$)
The rate of change of the center of mass velocity of an object, indicating how quickly its forward or backward speed is changing.
Example:
When a car speeds up, its linear acceleration increases.
Linear Displacement ($\Delta x_{cm}$)
The change in position of an object's center of mass, representing its overall translational distance moved.
Example:
If you walk 10 meters forward, your linear displacement is 10 meters.
Linear Velocity ($v_{cm}$)
The speed and direction of the center of mass of an object, describing its overall translational motion.
Example:
The linear velocity of a train is its speed along the tracks.
Moment of Inertia ($I$)
A measure of an object's resistance to changes in its rotational motion, analogous to mass in translational motion, and dependent on mass distribution.
Example:
A solid disk has a smaller moment of inertia than a hoop of the same mass and radius, making it easier to spin.
Radius ($r$)
The distance from the center of a circular or spherical object to its outer edge.
Example:
The radius of a bicycle wheel determines how far it travels with each full rotation.
Rolling Motion
A complex motion combining both translational movement of an object's center of mass and rotational movement about its center of mass.
Example:
A bowling ball rolling down the lane exhibits rolling motion, simultaneously moving forward and spinning.
Rolling With Slipping
A type of rolling motion where the point of contact between the rolling object and the surface moves relative to the surface, leading to energy dissipation due to kinetic friction.
Example:
When a car tire slips on ice, it spins faster than its forward motion would suggest, indicating rolling with slipping.
Rolling Without Slipping
A specific type of rolling motion where the point of contact between the rolling object and the surface is momentarily at rest, implying a direct relationship between linear and angular motion.
Example:
A bicycle wheel perfectly gripping the road and moving forward without skidding is an example of rolling without slipping.
Rotational Kinetic Energy ($K_{rot}$)
The energy an object possesses due to its spinning motion, dependent on its moment of inertia and angular velocity.
Example:
A figure skater spinning rapidly has significant rotational kinetic energy.
Rotational Motion
The spinning movement of an object around an axis, where different points on the object move at different speeds depending on their distance from the axis.
Example:
A spinning top demonstrates pure rotational motion around its central axis.
Static Friction (in ideal rolling)
A force that opposes the tendency of motion between two surfaces in contact when there is no relative motion between them, crucial for rolling without slipping.
Example:
The static friction between a car tire and the road allows the car to accelerate forward without spinning its wheels.
Total Kinetic Energy ($K_{tot}$)
The sum of an object's translational kinetic energy and its rotational kinetic energy, representing the total energy of motion for a rolling object.
Example:
To find the total kinetic energy of a rolling soccer ball, you add the energy from its forward movement and its spinning.
Translational Kinetic Energy ($K_{trans}$)
The energy an object possesses due to the motion of its center of mass, calculated as half its mass times the square of its center of mass velocity.
Example:
A sled sliding down a hill has translational kinetic energy due to its overall forward movement.
Translational Motion
The movement of an object from one point in space to another, where all points on the object move in the same direction and at the same speed.
Example:
A car driving straight down a highway is primarily undergoing translational motion.