Glossary
Angular Acceleration
The rate of change of an object's angular velocity, indicating how quickly its rotational speed is changing.
Example:
A merry-go-round speeding up from rest has a positive Angular Acceleration.
Angular Displacement
The angle through which an object rotates about an axis, measured in radians.
Example:
A door opening 90 degrees undergoes an Angular Displacement of π/2 radians.
Angular Velocity
The rate at which an object rotates or revolves relative to another point, measured in radians per second.
Example:
The blades of a ceiling fan have a constant Angular Velocity when spinning at a steady speed.
Energy Dissipation
The process by which mechanical energy is converted into other forms of energy, such as thermal energy (heat), due to non-conservative forces like kinetic friction or air resistance.
Example:
The brakes on a car cause Energy Dissipation, converting the car's kinetic energy into heat through friction.
Kinetic Friction
A force that opposes the relative motion between two surfaces that are sliding past each other. It always dissipates mechanical energy as heat.
Example:
When you push a box across a rough floor, Kinetic Friction acts against its motion, slowing it down.
Linear Acceleration
The rate of change of an object's linear velocity, indicating how quickly its speed or direction of motion is changing.
Example:
A car pressing the gas pedal experiences Linear Acceleration as its speed increases.
Linear Displacement
The straight-line distance and direction an object's center of mass moves from its initial position.
Example:
If a car travels 100 meters east, its Linear Displacement is 100 meters east.
Linear Velocity
The rate of change of an object's position in a straight line, including both speed and direction.
Example:
A sprinter's Linear Velocity is 10 m/s forward during a race.
Mechanical Energy Conservation
The principle that the total mechanical energy (sum of kinetic and potential energy) of a system remains constant if only conservative forces (like gravity) do work, and non-conservative forces (like kinetic friction) do no work.
Example:
A pendulum swinging back and forth, neglecting air resistance, demonstrates Mechanical Energy Conservation as its energy transforms between potential and kinetic forms.
Moment of Inertia
A measure of an object's resistance to changes in its rotational motion, analogous to mass in linear motion. It depends on the object's mass distribution relative to its axis of rotation.
Example:
A solid disk has a smaller Moment of Inertia than a hollow ring of the same mass and radius, making it easier to rotate.
Newton's Second Law (Linear)
States that the net force acting on an object is equal to the product of its mass and its linear acceleration (F=ma).
Example:
Pushing a shopping cart with a greater force results in a greater Linear Acceleration according to Newton's Second Law.
Newton's Second Law (Rotational)
States that the net torque acting on an object is equal to the product of its moment of inertia and its angular acceleration (τ=Iα).
Example:
Applying a larger torque to a bicycle wheel will result in a greater Angular Acceleration of the wheel, as described by Newton's Second Law (Rotational).
Rolling Motion
A type of motion where an object rotates about an axis while its center of mass also translates, often along a surface.
Example:
A bowling ball moving down the lane exhibits Rolling Motion, combining both its spin and its forward movement.
Rolling With Slipping
A condition where an object rolls while simultaneously sliding at its point of contact with the surface. In this case, kinetic friction is present and dissipates mechanical energy.
Example:
A car tire skidding on ice while still rotating is an example of Rolling With Slipping, leading to a loss of control and energy.
Rolling Without Slipping
An ideal condition where an object rolls such that there is no relative motion (sliding) at the point of contact with the surface. In this scenario, mechanical energy is conserved.
Example:
A bicycle wheel perfectly gripping the road demonstrates Rolling Without Slipping, allowing for efficient forward propulsion without energy loss due to friction.
Rotational Kinetic Energy
The energy an object possesses due to its rotational motion, calculated as 1/2Iω², where 'I' is the moment of inertia and 'ω' is angular velocity.
Example:
A spinning figure skater has Rotational Kinetic Energy that increases as she pulls her arms in, decreasing her moment of inertia and increasing her angular velocity.
Static Friction
A force that opposes the initiation of motion between two surfaces in contact and at rest relative to each other. In rolling without slipping, it acts as a constraint and does no work.
Example:
When you push a heavy box but it doesn't move, the Static Friction force is balancing your push.
Total Kinetic Energy
The sum of an object's translational kinetic energy (due to linear motion) and rotational kinetic energy (due to spinning motion). It represents the total energy of motion for an object that is both moving and rotating.
Example:
A spinning top that is also sliding across the floor possesses significant Total Kinetic Energy from both its linear movement and its rotation.
Translational Kinetic Energy
The energy an object possesses due to its linear motion, calculated as 1/2mv², where 'm' is mass and 'v' is linear velocity.
Example:
A car driving in a straight line has Translational Kinetic Energy proportional to its mass and the square of its speed.
Work-Energy Theorem
States that the net work done on an object equals the change in its kinetic energy. For systems with non-conservative forces, the work done by these forces accounts for changes in mechanical energy.
Example:
If a constant force pushes a block, the Work-Energy Theorem can be used to find the block's final speed based on the work done by the force.