Physics: Motion in 2D & Thermodynamics

Projectile Motion

The motion of an object launched into the air moving under the influence of gravity.

Horizontal Motion of a Projectile

Characterized by constant velocity, no acceleration, and ax = 0.

Vertical Motion of a Projectile

Characterized by constant acceleration due to gravity and changing velocity.

Horizontal Component of Initial Velocity

vx = vi cos(θ)

Vertical Component of Initial Velocity

viy = vi sin(θ)

Launch Angle for Maximum Range

45°

Uniform Circular Motion

Speed remains constant, direction changes continuously, and only centripetal acceleration exists.

Non-Uniform Circular Motion

Speed changes, and both tangential and centripetal accelerations are present.

Tangential Velocity Formula

v = rω

Centripetal Force Formula

Fc = m·v² / r

Thermodynamics

The study of moving or evolving heat.

Internal Energy

The sum of molecular kinetic energies and potential energy due to intermolecular processes.

Zeroth Law of Thermodynamics

Two bodies in thermal equilibrium with a third body are in thermal equilibrium with each other.

First Law of Thermodynamics

H = ΔU + W (Heat added increases internal energy and powers work).

Adiabatic Process

A thermodynamic process with no heat transfer into or out of the system (Q = 0).

Isochoric Process

A thermodynamic process that occurs at a constant volume.

Isobaric Process

A thermodynamic process that occurs at a constant pressure.

Isothermal Process

A thermodynamic process that occurs at a constant temperature.

Second Law (Kelvin-Planck Statement)

No heat engine can completely convert heat energy to work.

Second Law (Clausius Statement)

Heat flows naturally from hot objects to cold objects.

Third Law of Thermodynamics

It is impossible to attain absolute zero temperature.

Heat Engine

A device that converts heat energy to mechanical work using hot and cold reservoirs.

Moment of Inertia (I)

The property of a rotating body to resist change in its state of rotation; I = m·r².

Torque (τ)

The product of perpendicular force and the lever arm from the axis of rotation: τ = F·r.

Angular Momentum (L)

The product of moment of inertia and angular velocity (L = I·ω), conserved when net external torque is zero.

Impulse

The product of force and time during which it acts, equal to change in momentum (J = Δp).

Impulse-Momentum Theorem

States that the impulse of a net force is equal to the change in momentum of the body (F·t = m·Δv).

Elastic Collision

A collision in which both total momentum and total kinetic energy are conserved.

Inelastic Collision

A collision in which momentum is conserved, but kinetic energy is not conserved.

Center of Mass

The position where the total mass of a system can be considered concentrated for analyzing translational motion.

Newton's First Law (Law of Inertia)

An object remains at rest or in uniform motion unless acted upon by an external force.

Newton's Second Law (Law of Acceleration)

Force equals mass times acceleration (F = ma) or the rate of change of momentum.

Newton's Third Law (Law of Interaction)

For every action, there is an equal and opposite reaction.

Reference Frame

An observer's chosen coordinate system including an origin point used to measure position and motion.

Contact Forces

Forces that occur when two objects touch each other and transfer force through direct contact.

Non-Contact Forces

Forces that act on an object from a distance through a force field causing attraction or repulsion.

Free Body Diagram

A simple sketch of an object showing all external forces acting on it, used to analyze motion and equilibrium.

Work (Physics)

Work is done when a force acting on an object produces displacement.

Gravitational Potential Energy

Energy due to an object's position, calculated as PE = mgh.

Elastic Potential Energy

Energy due to configuration, common to springs, calculated as PE = (1/2)kx².

Kinetic Energy

Energy possessed by a body because of its motion, calculated as KE = (1/2)mv².

Conservative Force

A force where work is path-independent, closed-loop work is zero, and potential energy can be defined.

Non-Conservative Force

A force where work depends on the path taken and closed-loop work is not zero.

Stable Equilibrium

Equilibrium that occurs at a minimum potential energy, such as a marble inside a bowl.

Unstable Equilibrium

Equilibrium that occurs at a maximum potential energy, such as a ball on top of a hill.

Neutral Equilibrium

Equilibrium where potential energy remains approximately constant, such as a ball on a level floor.

Mechanical Power

The rate of doing work, expressed as P = W / t.