Glossary
Acceleration
The rate at which an object's velocity changes over time. This change can be in magnitude (speeding up or slowing down) or direction.
Example:
When a rocket launches, its acceleration is immense, rapidly increasing its upward velocity.
Amplitude (SHM)
The maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position.
Example:
If a swing moves 2 meters from its lowest point to its highest point, its amplitude is 2 meters.
Amplitude (Waves)
The maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position. For waves, it relates to the wave's energy.
Example:
A loud sound wave has a larger amplitude than a quiet one.
Angular Acceleration
The rate of change of angular velocity. It describes how quickly an object's rotational speed is increasing or decreasing.
Example:
When a bicycle wheel starts from rest and speeds up, it experiences angular acceleration.
Angular Displacement
The angle through which an object rotates around a fixed axis. It is measured in radians.
Example:
When a merry-go-round completes one full turn, it has undergone an angular displacement of 2π radians.
Angular Frequency (SHM)
A measure of the rate of oscillation in radians per second. It is related to frequency by $\omega = 2\pi f$ and period by $\omega = 2\pi/T$.
Example:
For a mass-spring system, the angular frequency determines how quickly the phase of the oscillation changes.
Angular Velocity
The rate of change of angular displacement, indicating how fast an object is rotating or revolving. It is a vector quantity, measured in radians per second.
Example:
A spinning top with a high angular velocity rotates very quickly.
Centripetal Acceleration
The acceleration directed towards the center of a circular path, which is necessary to keep an object moving in a circle. Its magnitude is given by $a_c = v^2/r$.
Example:
As a car rounds a sharp turn, the passengers feel pushed outwards, but the car is actually experiencing centripetal acceleration towards the center of the turn.
Centripetal Force
The net force that causes an object to move in a circular path, always directed towards the center of the circle. It is not a new type of force, but rather the net force resulting from other forces.
Example:
The gravitational pull of the Earth on the Moon provides the centripetal force that keeps the Moon in orbit.
Conservation of Mechanical Energy
States that in the absence of non-conservative forces (like friction or air resistance), the total mechanical energy (sum of kinetic and potential energy) of a system remains constant.
Example:
A swinging pendulum, ignoring air resistance, demonstrates the conservation of mechanical energy as its kinetic and potential energy continuously convert into each other.
Conservation of Momentum
States that in a closed system (no external forces), the total linear momentum of the system remains constant, even during collisions or explosions.
Example:
When a cannon fires a cannonball, the cannon recoils backward, demonstrating the conservation of momentum for the cannon-cannonball system.
Constructive Interference
Occurs when two waves combine in phase, resulting in a wave with a larger amplitude than the individual waves.
Example:
When two crests of water waves meet, they combine to form a larger crest through constructive interference.
Destructive Interference
Occurs when two waves combine out of phase, resulting in a wave with a smaller amplitude, or even zero amplitude if they completely cancel each other out.
Example:
If a crest of one wave meets a trough of another wave of equal amplitude, they will cancel each other out due to destructive interference.
Diffraction
The bending of waves as they pass around obstacles or through small openings. This phenomenon is more noticeable when the wavelength is comparable to the size of the obstacle or opening.
Example:
You can hear someone speaking around a corner because sound waves undergo diffraction.
Displacement
The change in an object's position, measured as a straight line from the initial to the final point. It is a vector quantity, meaning it has both magnitude and direction.
Example:
If you walk 5 meters east and then 5 meters west, your total displacement from your starting point is zero, even though you walked 10 meters.
Distance
The total length of the path traveled by an object. It is a scalar quantity, meaning it only has magnitude.
Example:
A marathon runner covers a distance of 42.195 kilometers, regardless of their starting and ending positions.
Doppler Effect
The apparent change in frequency or pitch of a wave (like sound or light) due to the relative motion between the source of the wave and the observer.
Example:
The pitch of an ambulance siren sounds higher as it approaches you and lower as it moves away, illustrating the Doppler Effect.
Elastic Collisions
Collisions in which both momentum and kinetic energy are conserved. Objects bounce off each other without deformation or heat loss.
Example:
The collision between two billiard balls is a close approximation of an elastic collision.
Elastic Potential Energy
The energy stored in an elastic material, such as a spring, when it is stretched or compressed. It depends on the spring constant and the displacement ($PE_s = \frac{1}{2}kx^2$).
Example:
A compressed spring in a pogo stick stores elastic potential energy.
Equilibrium
A state where the net force acting on an object is zero. This means the object is either at rest or moving with a constant velocity.
Example:
A chandelier hanging motionless from the ceiling is in equilibrium, as the upward tension balances the downward force of gravity.
Free-Body Diagrams (FBDs)
A visual representation of all external forces acting on a single object. It simplifies complex scenarios by isolating the object and showing forces as arrows.
Example:
Drawing a free-body diagram for a car on an incline helps visualize the gravitational, normal, and friction forces acting on it.
Frequency (SHM)
The number of complete oscillations or cycles that occur per unit of time. It is the reciprocal of the period.
Example:
A guitar string vibrating 440 times per second has a frequency of 440 Hz.
Frequency (Waves)
The number of complete wave cycles that pass a point per unit of time. It is measured in Hertz (Hz).
Example:
A high-pitched sound has a higher frequency than a low-pitched sound.
Friction
A force that opposes motion or attempted motion between surfaces in contact. It can be static (preventing motion) or kinetic (opposing motion).
Example:
When you slide a box across the floor, the resistance you feel is due to friction between the box and the floor.
Gravitational Potential Energy
The energy an object possesses due to its position in a gravitational field. It depends on mass, height, and the acceleration due to gravity ($PE_g = mgh$).
Example:
A roller coaster car at the top of a hill has maximum gravitational potential energy.
Gravity (Force)
The attractive force between any two objects with mass. On Earth, it refers to the force exerted by the Earth on an object, causing it to accelerate downwards ($F_g = mg$).
Example:
An apple falling from a tree is pulled down by the force of gravity.
Impulse
The change in an object's momentum, caused by a force acting over a period of time ($J = \Delta p = F\Delta t$). It is also the area under a force-time graph.
Example:
An airbag increases the time over which a force acts during a collision, reducing the impulse and thus the force on the occupant.
Inelastic Collisions
Collisions in which momentum is conserved, but kinetic energy is not. Some kinetic energy is converted into other forms, such as heat or sound.
Example:
A car crash where the vehicles crumple and deform is an example of an inelastic collision.
Interference
The phenomenon that occurs when two or more waves overlap and combine to form a new wave of greater, lower, or the same amplitude. It can be constructive or destructive.
Example:
Noise-canceling headphones work by creating sound waves that cause destructive interference with incoming ambient noise.
Kinematic Equations
A set of equations used to describe the motion of objects under constant acceleration. They relate displacement, initial velocity, final velocity, acceleration, and time.
Example:
You can use the kinematic equations to predict how far a dropped ball will fall in a certain amount of time.
Kinetic Energy
The energy an object possesses due to its motion. It depends on the object's mass and its speed ($KE = \frac{1}{2}mv^2$).
Example:
A speeding bullet has a large amount of kinetic energy due to its high velocity.
Longitudinal Waves
Waves in which the particles of the medium oscillate parallel to the direction of wave propagation.
Example:
Sound waves are longitudinal waves because air molecules vibrate back and forth in the same direction the sound travels.
Mass-Spring System
A system consisting of a mass attached to a spring, capable of undergoing simple harmonic motion. Its period depends on the mass and spring constant.
Example:
A car's suspension system uses a mass-spring system to absorb shocks from the road.
Moment of Inertia
A measure of an object's resistance to changes in its rotational motion. It depends on the object's 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.
Momentum
A measure of an object's mass in motion, defined as the product of its mass and velocity ($p = mv$). It is a vector quantity.
Example:
A bowling ball has more momentum than a tennis ball moving at the same speed because of its greater mass.
Newton's First Law (Inertia)
States that an object at rest stays at rest, and an object in motion stays in motion with the same velocity, unless acted upon by a net external force.
Example:
When a bus suddenly brakes, passengers lurch forward due to their inertia, resisting the change in motion.
Newton's Second Law
States that the net force acting on an object is equal to the product of its mass and acceleration ($F_{net} = ma$). This law quantifies the relationship between force, mass, and motion.
Example:
Pushing a small toy car requires less force to achieve the same acceleration than pushing a heavy truck, illustrating Newton's Second Law.
Newton's Second Law for Rotation
States that the net torque acting on an object is equal to the product of its moment of inertia and angular acceleration ($ au_{net} = I\alpha$). It is the rotational analogue of $F_{net} = ma$.
Example:
Applying a net torque to a bicycle wheel will cause it to undergo angular acceleration, as described by Newton's Second Law for Rotation.
Newton's Third Law
States that for every action, there is an equal and opposite reaction. Forces always occur in pairs acting on two different objects.
Example:
When a swimmer pushes water backward, the water pushes the swimmer forward with an equal and opposite force, demonstrating Newton's Third Law.
Non-Conservative Forces
Forces that dissipate mechanical energy from a system, meaning the work done by these forces depends on the path taken. Examples include friction and air resistance.
Example:
When a car brakes, non-conservative forces like friction convert the car's kinetic energy into heat and sound.
Normal Force
The component of a contact force perpendicular to the surface that an object is resting on or in contact with. It prevents objects from passing through surfaces.
Example:
When a book rests on a table, the table exerts an upward normal force on the book, balancing the force of gravity.
Perfectly Inelastic Collisions
A type of inelastic collision where the colliding objects stick together after impact and move as a single combined mass. Kinetic energy loss is maximized in this type of collision.
Example:
When a bullet embeds itself in a block of wood, it's a perfectly inelastic collision because they move together afterward.
Period (SHM)
The time it takes for one complete oscillation or cycle of a vibrating system. It is the reciprocal of frequency.
Example:
If a pendulum swings back and forth once every 2 seconds, its period is 2 seconds.
Potential Energy
Stored energy an object possesses due to its position or configuration. Common types include gravitational and elastic potential energy.
Example:
A stretched rubber band stores potential energy that can be converted into kinetic energy when released.
Power
The rate at which work is done or energy is transferred. It is calculated as work divided by time ($P = W/\Delta t$) or force times velocity ($P = Fv$).
Example:
A powerful engine can do a large amount of work in a short amount of time.
Projectile Motion
The motion of an object thrown or projected into the air, subject only to the acceleration of gravity. It is analyzed by separating horizontal and vertical components.
Example:
The path of a basketball shot towards the hoop is an example of projectile motion.
Reflection
The bouncing back of a wave when it encounters a boundary or surface that it cannot pass through.
Example:
An echo is an example of sound wave reflection off a distant surface.
Refraction
The bending of a wave as it passes from one medium into another, due to a change in its speed.
Example:
A straw in a glass of water appears bent at the water's surface due to the refraction of light.
Simple Harmonic Motion (SHM)
A type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium and acts in the opposite direction. It results in sinusoidal oscillations.
Example:
A mass oscillating on an ideal spring demonstrates simple harmonic motion.
Simple Pendulum
An idealized pendulum consisting of a point mass suspended by a massless, inextensible string. For small angles, its motion approximates simple harmonic motion.
Example:
The swinging bob of a grandfather clock acts as a simple pendulum.
Speed
The rate at which an object covers distance over time. It is a scalar quantity, only indicating how fast an object is moving.
Example:
A cheetah can reach a top speed of 120 km/h, making it the fastest land animal.
Spring Force
The restoring force exerted by a spring, which is proportional to its displacement from equilibrium and acts in the opposite direction of the displacement ($F_s = -kx$).
Example:
When you compress a toy dart gun, the spring force builds up, ready to launch the dart.
Superposition
The principle that when two or more waves overlap, the resultant displacement at any point and at any instant is the vector sum of the displacements of the individual waves at that point.
Example:
When two ripples on a pond meet, they momentarily combine according to the principle of superposition.
Tension
The pulling force transmitted axially by a string, cable, chain, or similar one-dimensional continuous object. It acts along the length of the object.
Example:
The tension in the rope of a tug-of-war game is the force pulling each team.
Torque
A rotational equivalent of force, which causes or tends to cause rotation. It depends on the applied force, the distance from the pivot point, and the angle between them.
Example:
Using a long wrench to loosen a stubborn bolt applies more torque than using a short wrench with the same force.
Transverse Waves
Waves in which the particles of the medium oscillate perpendicular to the direction of wave propagation.
Example:
Ripples on the surface of water or light waves are examples of transverse waves.
Velocity
The rate at which an object's displacement changes over time. It is a vector quantity, indicating 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.
Wave Speed
The speed at which a wave propagates through a medium. It is related to wavelength and frequency by the equation $v = f\lambda$.
Example:
The wave speed of light in a vacuum is approximately m/s.
Wavelength
The spatial period of a wave, which is the distance over which the wave's shape repeats. It is the distance between two consecutive crests or troughs.
Example:
The distance between two consecutive peaks of an ocean wave is its wavelength.
Work
The transfer of energy that occurs when a force causes a displacement of an object in the direction of the force. It is calculated as $W = Fd\cos heta$.
Example:
Lifting a heavy box onto a shelf requires you to do work against gravity.
Work-Energy Theorem
States that the net work done on an object is equal to the change in its kinetic energy ($W_{net} = \Delta KE$). It links the concepts of work and energy.
Example:
If a car's engine does positive work on it, the car's kinetic energy will increase, as per the Work-Energy Theorem.