Glossary
Acceleration
Acceleration (a) is a vector quantity that describes the rate at which an object's velocity changes over time, indicating a change in speed, direction, or both.
Example:
When a roller coaster speeds up as it plunges down a hill, it experiences significant positive acceleration.
Amplitude (SHM)
Amplitude (A) in Simple Harmonic Motion is the maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position.
Example:
If a spring is stretched 10 cm from its resting position and released, the amplitude of its oscillation is 10 cm.
Angular Momentum
Angular momentum (L) is a vector quantity that describes the 'quantity of rotational motion' of an object, conserved in the absence of external torques.
Example:
When a diver tucks into a ball mid-air, they decrease their rotational inertia, causing their angular velocity to increase to conserve angular momentum.
Centripetal Acceleration
Centripetal acceleration is the acceleration directed towards the center of a circular path, responsible for changing the direction of an object's velocity.
Example:
As a car rounds a curve, the centripetal acceleration keeps it moving along the curved path rather than continuing in a straight line.
Centripetal Force
Centripetal force is the net force required to keep an object moving in a circular path, always directed towards the center of the circle.
Example:
The tension in a string swinging a ball in a circle provides the centripetal force necessary to maintain its circular motion.
Connected Objects
Connected objects refer to systems where multiple objects are linked together, often by strings or ropes, and their motions are interdependent.
Example:
Analyzing the motion of an Atwood machine, where two masses are connected by a string over a pulley, involves understanding connected objects.
Conservation of Linear Momentum
The Conservation of Linear Momentum principle states that in a closed system (no external forces), the total linear momentum of the system remains constant.
Example:
When two billiard balls collide on a frictionless table, their total linear momentum before the collision is equal to their total linear momentum after the collision.
Conservation of Mechanical Energy
The Conservation of Mechanical Energy principle states that in the absence of non-conservative forces like friction or air resistance, the total mechanical energy of a system remains constant.
Example:
A roller coaster car gliding down a frictionless track demonstrates the conservation of mechanical energy, as potential energy converts to kinetic energy and vice versa.
Displacement
Displacement (Δx) is a vector quantity representing the change in an object's position from its starting point to its ending point.
Example:
If you walk 5 meters east and then 5 meters west, your total distance traveled is 10 meters, but your displacement is 0 meters.
Elastic Collision
An elastic collision is a type of collision where both momentum and kinetic energy are conserved.
Example:
The collision between two perfectly bouncy superballs, where no energy is lost as heat or sound, would be an ideal elastic collision.
Free-Body Diagrams
Free-body diagrams are visual representations that show all the forces acting on a single object, isolated from its surroundings.
Example:
Before solving a problem involving a block on an inclined plane, drawing a free-body diagram helps visualize the gravitational, normal, and frictional forces.
Frequency (f)
Frequency (f) is the number of complete cycles or oscillations that occur per unit of time, and it is the reciprocal of the period.
Example:
If a speaker vibrates 440 times per second, its frequency is 440 Hertz.
Friction
Friction is a force that opposes motion or attempted motion between two surfaces in contact.
Example:
When you slide a box across the floor, the resistance you feel is due to friction between the box and the floor.
Gravitational Field
A gravitational field is a region of space around a mass where another mass would experience a gravitational force.
Example:
The Earth creates a gravitational field around it, which is why satellites remain in orbit.
Gravity
Gravity is a fundamental force of attraction between any two objects with mass, causing them to accelerate towards each other.
Example:
An apple falling from a tree is pulled towards the Earth due to the force of gravity.
Impulse
Impulse (J) is the change in an object's momentum, equal to the average net force applied to the object multiplied by the time interval over which the force acts.
Example:
When a baseball bat hits a ball, the large force applied for a short time creates a significant impulse, changing the ball's momentum.
Inclined Planes
Inclined planes are flat surfaces tilted at an angle to the horizontal, often used to analyze forces and motion in a gravitational field.
Example:
A ramp used to load furniture into a moving truck is an inclined plane, making it easier to move heavy objects.
Inelastic Collision
An inelastic collision is a type of collision where momentum is conserved, but kinetic energy is not conserved, typically due to energy conversion into other forms like heat or sound.
Example:
When a car crashes into a wall, it's an inelastic collision because kinetic energy is lost as deformation, heat, and sound.
Kinematic Equations
Kinematic equations are a set of mathematical formulas used to describe the motion of objects with constant acceleration.
Example:
You can use kinematic equations to predict how far a dropped ball will fall in a certain amount of time.
Kinetic Energy
Kinetic energy (KE) is the energy an object possesses due to its motion.
Example:
A speeding bullet has a large amount of kinetic energy due to its high velocity.
Law of Universal Gravitation
The Law of Universal Gravitation states that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Example:
The Law of Universal Gravitation explains why the Moon orbits the Earth and why objects fall to the ground.
Lever Arm
The lever arm is the perpendicular distance from the axis of rotation to the line of action of the force that causes torque.
Example:
When opening a door, pushing further from the hinges increases the lever arm, making it easier to apply torque.
Mass-Spring System
A mass-spring system consists of a mass attached to a spring, which, when displaced from equilibrium, undergoes simple harmonic motion.
Example:
A car's suspension system uses a mass-spring system to absorb shocks and provide a smooth ride.
Momentum
Momentum (p) is a vector quantity defined as the product of an object's mass and its velocity, representing its 'quantity of motion'.
Example:
A bowling ball rolling down the lane has more momentum than a tennis ball moving at the same speed because of its greater mass.
Newton's First Law
Newton's First Law, also known as the Law of Inertia, states that an object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by a net force.
Example:
A soccer ball sitting motionless on the field will remain at rest until a player kicks it, illustrating Newton's First Law.
Newton's Second Law
Newton's Second Law states that the net force acting on an object is equal to the product of its mass and acceleration ($F_{net} = ma$).
Example:
Pushing a small toy car with a certain force will cause it to accelerate more than pushing a large truck with the same force, as described by Newton's Second Law.
Newton's Second Law for Rotation
Newton's Second Law for Rotation states that the net torque acting on an object is equal to the product of its rotational inertia and its angular acceleration (τ_net = Iα).
Example:
Applying a larger torque to a bicycle wheel will result in a greater angular acceleration, as described by Newton's Second Law for Rotation.
Newton's Third Law
Newton's Third Law states that for every action, there is an equal and opposite reaction.
Example:
When a rocket expels hot gas downwards, the gas exerts an equal and opposite force upwards on the rocket, propelling it into space, which is an application of Newton's Third Law.
Normal Force
Normal force is the component of a contact force exerted by a surface on an object that is perpendicular to the surface.
Example:
When a book rests on a table, the table exerts an upward normal force on the book, preventing it from falling through.
Orbital Motion
Orbital motion describes the curved path of an object, such as a planet or satellite, around a star or another celestial body due to gravity.
Example:
The Earth's yearly journey around the Sun is a prime example of orbital motion.
Perfectly Inelastic Collision
A perfectly inelastic collision is a type of inelastic collision where the colliding objects stick together after impact and move as a single combined mass.
Example:
When a bullet embeds itself in a block of wood and the two move together, it's a perfectly inelastic collision.
Period (T)
Period (T) is the time it takes for one complete cycle or oscillation of a repeating motion.
Example:
The period of a pendulum is the time it takes for the pendulum to swing back and forth once.
Potential Energy (Elastic)
Elastic potential energy (PEs) is the energy stored in an elastic material, such as a spring, when it is stretched or compressed.
Example:
A stretched slingshot stores elastic potential energy that is converted into kinetic energy when released.
Potential Energy (Gravitational)
Gravitational potential energy (PEg) is the energy an object possesses due to its position in a gravitational field, typically its height above a reference point.
Example:
A diver standing on a high platform has significant gravitational potential energy before jumping into the water.
Power
Power (P) is the rate at which work is done or energy is transferred.
Example:
A powerful engine can accelerate a car from 0 to 60 mph in a very short time, indicating high power output.
Projectile Motion
Projectile motion is the motion of an object thrown or projected into the air, subject only to the acceleration of gravity.
Example:
The arc a basketball makes when shot towards the hoop is an example of projectile motion.
Relative Motion
Relative motion describes the motion of an object as observed from a particular frame of reference, which itself may be in motion.
Example:
When you're on a moving train, a person walking down the aisle has a different relative motion with respect to you than they do with respect to someone standing on the ground outside the train.
Rotational Inertia (Moment of Inertia)
Rotational inertia (I), also known as moment of inertia, is a measure of an object's resistance to changes in its rotational motion.
Example:
A figure skater pulls their arms in to decrease their rotational inertia, allowing them to spin faster.
Rotational Kinematic Equations
Rotational kinematic equations are a set of formulas used to describe the rotational motion of objects with constant angular acceleration, analogous to linear kinematic equations.
Example:
You can use rotational kinematic equations to calculate how many revolutions a spinning top makes before coming to rest.
Rotational Kinetic Energy
Rotational kinetic energy (KE_rot) is the energy an object possesses due to its rotation.
Example:
A spinning flywheel stores rotational kinetic energy that can be used to power machinery.
Simple Harmonic Motion (SHM)
Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position and acts in the opposite direction.
Example:
The rhythmic bobbing of a mass attached to a spring, or the swing of a pendulum for small angles, are classic examples of Simple Harmonic Motion.
Simple Pendulum
A simple pendulum consists of a point mass suspended by a massless, inextensible string from a fixed pivot, undergoing simple harmonic motion for small angles of displacement.
Example:
The swinging bob of a grandfather clock approximates a simple pendulum.
Tension
Tension is the pulling force transmitted axially by means of a string, cable, chain, or similar one-dimensional continuous object.
Example:
The force in a rope supporting a rock climber as they ascend a cliff is an example of tension.
Torque
Torque (τ) is the rotational equivalent of force, causing an object to rotate or change its rotational motion.
Example:
Using a wrench to tighten a bolt applies torque, causing the bolt to turn.
Total Mechanical Energy
Total mechanical energy (E) is the sum of an object's kinetic energy and potential energy.
Example:
For a swinging pendulum, its total mechanical energy is the sum of its kinetic energy at the bottom of the swing and its potential energy at the highest points.
Velocity
Velocity (v) is a vector quantity that describes the rate at which an object's displacement changes over time, including both speed and direction.
Example:
A car traveling at 60 km/h north has a different velocity than a car traveling at 60 km/h south, even though their speeds are the same.
Work
Work (W) is the transfer of energy that occurs when a force causes a displacement of an object in the direction of the force.
Example:
Lifting a heavy box from the floor to a shelf requires work to be done against gravity.
Work-Energy Theorem
The Work-Energy Theorem states that the net work done on an object is equal to the change in its kinetic energy.
Example:
If you push a box across a floor, the work-energy theorem relates the work you do to the increase in the box's speed.