PHYSICS A

Kinematics, Dynamics, Energy and Momentum, Circular Motion

Mechanics

The branch of physics that deals with the motion of objects and the forces that cause the motion

Kinematics

The study of motion without considering its causes; describes how objects move

Kinematic Equations

A set of four equations used to calculate motion variables like displacement, velocity, acceleration, and time

Displacement

The change in position of an object; a vector quantity (has magnitude and direction)

Velocity

The rate of change of displacement; a vector quantity (includes direction)

Speed

The rate of change of distance; a scalar quantity (no direction)

Acceleration

The rate of change of velocity over time; can be positive (speeding up) or negative (slowing down)

Uniform Motion

Motion with constant velocity (no acceleration)

Uniformly Accelerated Motion

Motion with constant acceleration (velocity changes at a constant rate)

Kinematic Equation 1

v = u + at (final velocity = initial velocity + acceleration × time)

Kinematic Equation 2

s = ut + ½at² (displacement = initial velocity × time + ½ × acceleration × time²)

Kinematic Equation 3

v² = u² + 2as (final velocity squared = initial velocity squared + 2 × acceleration × displacement)

Kinematic Equation 4

s = (u + v)t / 2 (displacement = average velocity × time)

Motion in One Dimension

Motion along a straight line; described using one coordinate axis (e.g., horizontal or vertical)

Motion in Two Dimensions

Motion in a plane; requires both x and y coordinates; includes projectile motion

Projectile Motion

A form of two-dimensional motion where an object moves under the influence of gravity only

Horizontal Motion

In projectile motion, the horizontal velocity remains constant (no horizontal acceleration)

Vertical Motion

In projectile motion, vertical motion is affected by gravity and follows kinematic equations

Free Fall

A special case of vertical motion under gravity; acceleration = 9.8 m/s² downward

Relative Velocity

The velocity of an object as observed from a particular frame of reference

Dynamics

The branch of mechanics that deals with the forces and their effect on motion

Force

A push or pull acting on an object; a vector quantity measured in newtons (N)

Vector

A quantity that has both magnitude and direction (e.g., force, velocity, acceleration)

Scalar

A quantity that has only magnitude and no direction (e.g., mass, speed, temperature)

Newton's First Law

An object remains at rest or in uniform motion unless acted on by an external force (Law of Inertia)

Newton's Second Law

F = ma (Force = mass × acceleration); describes how force affects motion

Newton's Third Law

For every action, there is an equal and opposite reaction

Net Force

The overall force acting on an object after all forces are combined

Balanced Forces

Forces that are equal in magnitude and opposite in direction; no change in motion

Unbalanced Forces

Forces that cause a change in motion (acceleration)

Statics

The study of forces in systems that are in equilibrium (no movement or constant velocity)

Equilibrium

State in which the net force and net torque on a system are zero

Friction

A force that opposes the motion of one surface over another

Static Friction

Friction that prevents an object from starting to move

Kinetic Friction

Friction between surfaces in relative motion

Coefficient of Friction

A unitless ratio that describes the strength of friction between two surfaces

Energy

The capacity to do work; measured in joules (J)

Kinetic Energy

Energy of motion; KE = ½mv²

Potential Energy

Stored energy due to position; gravitational PE = mgh

Mechanical Energy

The sum of kinetic and potential energy in a system

Work

The transfer of energy through motion; W = F × d × cos(θ)

Power

The rate at which work is done; P = W/t; measured in watts (W)

Simple Machine

A device that changes the direction or magnitude of a force (e.g., lever, pulley, inclined plane)

Mechanical Advantage

Ratio of output force to input force in a machine

Momentum

A measure of an object’s motion; momentum = mass × velocity

Impulse

A change in momentum; impulse = force × time

Law of Conservation of Momentum

Total momentum in a closed system remains constant unless acted on by external forces

Law of Conservation of Energy

Energy cannot be created or destroyed, only transformed from one form to another

Elastic Collision

A collision where kinetic energy and momentum are conserved

Inelastic Collision

A collision where momentum is conserved but kinetic energy is not

Circular Motion

The motion of an object along a curved path or a circle

Uniform Circular Motion

Motion in a circle with constant speed but changing direction (thus changing velocity)

Tangential Velocity

Velocity that is tangent to the circle at any point; v = 2πr / T

Centripetal Acceleration

Acceleration directed toward the center of the circle; a = v² / r

Centripetal Force

The net force that causes circular motion; directed toward the center; Fc = mv² / r

Period (T)

Time it takes to complete one full revolution; measured in seconds

Frequency (f)

Number of revolutions per second; f = 1 / T

Radius (r)

The distance from the center of the circle to the moving object

Relationship of Speed to Radius and Force

As radius increases, for constant speed, less centripetal force is required

Effect of Mass on Centripetal Force

More mass means more force is needed to maintain circular motion at a given speed and radius

No Centrifugal Force

“Centrifugal force” is a perceived force due to inertia in the rotating frame; it is not a real force

Angular Velocity (ω)

Rate of change of the angle; ω = 2π / T

Unit of Centripetal Force

Newton (N), since it is a force