Glossary
Angle of Rotation (Δθ)
The angular displacement of a rotating object, measured in radians, indicating how much the object has turned.
Example:
When a door opens, the angle of rotation describes how far it has swung from its closed position.
Angular Acceleration
The rate at which an object's angular velocity changes over time, indicating how quickly its rotation speeds up or slows down, typically in radians per second squared.
Example:
When a bicycle wheel is spun faster and faster, it undergoes positive angular acceleration.
Angular Acceleration (α)
The rate of change of angular velocity, indicating how quickly an object's rotational speed is increasing or decreasing.
Example:
When a fan is turned on and speeds up, it undergoes angular acceleration.
Angular Displacement
The angle through which a point or line has been rotated in a specified direction around a fixed axis, typically measured in radians.
Example:
A door opening 90 degrees has an angular displacement of π/2 radians.
Angular Displacement (θ)
The change in angular position of a rotating object, measured from a reference line to its final position.
Example:
If a clock's minute hand moves from 12 to 3, its angular displacement is 90 degrees or π/2 radians.
Angular Velocity
The rate at which an object rotates or revolves around an axis, measured as the change in angular displacement over time, typically in radians per second.
Example:
A merry-go-round completing one full rotation every 5 seconds has a constant angular velocity of 2π/5 rad/s.
Angular Velocity (ω)
The rate at which an object rotates or revolves, representing the change in angular displacement over time.
Example:
A fast-spinning blender blade has a high angular velocity.
Arc Length (s)
The linear distance along the curved path of a circle, often used to describe the distance a point travels during angular displacement.
Example:
The distance a runner covers on a curved track is an arc length.
Center of Mass
The unique point where the weighted average of all the mass of a system is located, representing the average position of all the mass that makes up the object.
Example:
For a uniformly dense sphere, the center of mass is exactly at its geometric center.
Clockwise
A direction of rotation that mimics the movement of the hands on a traditional analog clock.
Example:
When tightening a screw, you typically turn it in a clockwise direction.
Counterclockwise
A direction of rotation opposite to the movement of the hands on a traditional analog clock.
Example:
To loosen a bolt, you usually turn it in a counterclockwise direction.
Displacement (linear)
The change in position of an object in a straight line, measured as the shortest distance from the initial to the final position.
Example:
If you walk 5 meters east, your linear displacement is 5 meters east.
Free-body Diagram
A visual representation of an object, showing all external forces acting upon it, typically drawn as vectors originating from the object's center of mass.
Example:
To analyze the forces on a block sliding down a ramp, you would first draw a free-body diagram showing gravity, normal force, and friction.
Linear Distance Traveled During Rotation (Δs)
The actual path length covered by a point on a rotating object as it moves along a circular arc.
Example:
If a car tire rotates, the distance a specific point on its tread covers on the road is its linear distance traveled during rotation.
Linear Motion
Motion that occurs along a straight line or path, where an object's position changes in one or more dimensions without rotation.
Example:
A car driving straight down a highway demonstrates linear motion.
Linear Velocity (v)
The instantaneous speed and direction of a point moving along a straight or curved path, representing how fast a point on a rotating object is moving tangentially.
Example:
A point on the edge of a spinning record has a higher linear velocity than a point closer to the center.
Moment of Inertia
A measure of an object's resistance to changes in its rotational motion, analogous to mass in linear motion, and dependent on its mass distribution and the axis of rotation.
Example:
A spinning ice skater pulls their arms in to decrease their moment of inertia, causing them to spin faster.
Net Force Equation
A mathematical statement that equates the vector sum of all external forces acting on an object to the product of its mass and acceleration, based on Newton's Second Law.
Example:
For a car accelerating, the engine's thrust minus air resistance and friction equals the car's mass times its acceleration, forming the net force equation.
Net Torque Equation
A mathematical statement that equates the sum of all external torques acting on an object to the product of its moment of inertia and angular acceleration.
Example:
When a wrench turns a bolt, the applied force times the lever arm equals the bolt's moment of inertia times its angular acceleration, as described by the net torque equation.
Radians
The standard unit for measuring angles in physics, defined as the angle subtended at the center of a circle by an arc equal in length to the radius.
Example:
To calculate the linear speed of a spinning top, you must convert its revolutions per minute into radians per second.
Radius (r)
The distance from the axis of rotation to a specific point on the rotating object.
Example:
The radius of a Ferris wheel determines how far each passenger is from its central axle.
Radius (r)
The distance from the center of a circle or sphere to any point on its circumference or surface.
Example:
For a point on the edge of a spinning record, the radius is the distance from the center spindle to that point.
Rigid System
A system where the distances between all constituent particles remain constant during motion, meaning it maintains its shape and size while rotating.
Example:
A solid bicycle wheel is considered a rigid system because its spokes and rim don't deform as it spins.
Rigid System
A system of particles or a body where the distance between any two given points remains constant, meaning it does not deform under applied forces.
Example:
A solid, unbending metal rod rotating about its center can be considered a rigid system.
Rolling without Slipping
A condition where a rolling object's point of contact with the surface is instantaneously at rest, meaning there is no relative motion or friction at that point.
Example:
A car tire moving perfectly on dry pavement is an example of rolling without slipping.
Rotational Motion
The motion of an object around an axis or center, where all points on the object move in circular paths.
Example:
A spinning rotational motion of a figure skater as they twirl on ice.
Rotational Motion
Motion where an object spins or rotates around an axis, with all points on the object moving in circular paths.
Example:
A spinning figure skater exhibits rotational motion around a vertical axis.
Tangential Acceleration
The component of linear acceleration that is tangent to the circular path of a rotating object, indicating a change in its linear speed.
Example:
As a car speeds up while going around a circular track, it experiences tangential acceleration.
Tangential Acceleration (a_t)
The component of acceleration that is tangent to the circular path of a rotating object, indicating the rate of change of its linear speed.
Example:
When a car speeds up while turning a corner, it experiences tangential acceleration in the direction of its motion.
Uniform Angular Acceleration
A state where every point within a rigid rotating system experiences the same rate of change in angular velocity.
Example:
As a merry-go-round speeds up from rest, all riders experience the same uniform angular acceleration.
Uniform Angular Motion
The motion of a rigid body rotating with a constant angular velocity, meaning its angular speed and direction of rotation do not change.
Example:
A perfectly balanced ceiling fan spinning at its highest setting exhibits uniform angular motion.
Uniform Angular Velocity
A state where every point within a rigid rotating system has the same angular speed and direction of rotation.
Example:
All parts of a spinning CD, from the center to the edge, share the same uniform angular velocity.
Velocity (linear)
The rate at which an object's position changes in a straight line, including both its speed and direction.
Example:
A ball thrown upwards with a speed of 10 m/s has an initial linear velocity of 10 m/s upwards.