Applied Physics Cheat Sheet: Mechanics and Thermal Physics
Applied Physics Cheat Sheet (Ch. 7–17)
Side A — Mechanics
Work
Work: The product of force and displacement in the direction of the force.
Important ideas:
- No displacement → no work
- Force perpendicular to motion → no work
Formula: W = Fd
Units: Joules (J)
Power
Power: The rate at which work is done or energy is transferred.
Formula: P = W / t
Units: Watts (W)
Energy
Energy: The ability to do work.
Energy can change forms, but total energy remains constant (Conservation of Energy).
Forms include:
- Kinetic
- Potential
- Thermal
- Chemical
- Nuclear
Potential Energy
Potential Energy: Stored energy due to position or configuration.
Gravitational potential energy depends on height.
Formula: PE = mgh
Kinetic Energy
Kinetic Energy: Energy an object has because of its motion.
Formula: KE = ½mv²
Important concept: Velocity is squared; small speed changes greatly affect KE.
Work–Energy Theorem
Definition: The net work done on an object equals the change in its kinetic energy.
Formula: W = ΔKE
Often used in:
- Stopping distance
- Friction problems
Rotational Motion
Rotational Motion: Motion of an object around an axis.
Examples: Wheel, fan, planets.
Tangential Speed
Speed of an object along the edge of a rotating circle.
Units: m/s
Angular Speed
Rate at which an object rotates.
Units: rad/s
Relation: v = rω
Torque
Torque: The turning effect of a force about an axis.
Formula: τ = rF
Maximum torque occurs when force is perpendicular.
Examples: Wrench, door, seesaw.
Moment of Inertia
Moment of inertia: The rotational equivalent of mass, representing resistance to rotational acceleration.
Point mass formula: I = mr²
Angular Momentum
Angular Momentum: A quantity describing rotational motion, equal to moment of inertia times angular velocity.
Formula: L = Iω
Rule: Angular momentum is conserved unless external torque acts.
Example: Figure skater spins faster when arms are pulled in.
Centripetal Force
Centripetal Force: The inward force required to keep an object moving in a circular path.
Formula: F = mv² / r
Possible sources:
- Tension
- Gravity
- Friction
- Normal force
Gravity
Gravity: The force of attraction between any two masses.
Universal Law of Gravitation
Formula: F = G(m₁m₂) / r²
Important concept: Inverse-square law. If distance doubles, force becomes ¼.
Weight
Weight is the gravitational force acting on an object.
Formula: F = mg
Projectile Motion
Projectile: An object that moves only under the influence of gravity.
Key rules:
- Horizontal velocity is constant
- Gravity affects vertical motion only
- Motions are independent
Trajectory: Parabola
Maximum range (level ground): 45°
Side B — Matter & Thermal Physics
Atomic Structure
Atom: Smallest unit of an element that retains chemical properties.
Structure:
- Protons (+)
- Neutrons (0)
- Electrons (−)
Atomic Number
Number of protons in the nucleus. Determines the element.
Isotopes
Atoms of the same element with different numbers of neutrons.
Density
Density: Mass per unit volume.
Formula: ρ = m / V
Higher density → sinks; Lower density → floats.
Hooke’s Law
Hooke’s Law: The force required to stretch or compress a spring is proportional to the displacement from its equilibrium position.
Formula: F = kx
Where k = spring constant and x = displacement. Valid only within the elastic limit.
Pressure
Pressure: Force applied per unit area.
Formula: P = F / A
Units: Pascal (Pa)
Pressure in Fluids
Pressure increases with depth in a fluid.
Formula: P = ρgh
Pascal’s Principle
Definition: A change in pressure applied to an enclosed fluid is transmitted equally throughout the fluid and to the walls of the container.
Hydraulic machines use this to multiply force. Formula: F₁/A₁ = F₂/A₂
Examples: Hydraulic lifts, car jacks.
Buoyant Force
Buoyant Force: The upward force exerted by a fluid on an object immersed in it.
Archimedes’ Principle
Definition: An object submerged in a fluid experiences a buoyant force equal to the weight of the fluid it displaces.
Rules:
- Buoyant > weight → object rises
- Buoyant < weight → object sinks
- Buoyant = weight → object floats
Floating objects displace their own weight of fluid.
Boyle’s Law
Definition: For a fixed amount of gas at constant temperature, pressure is inversely proportional to volume.
Formula: P₁V₁ = P₂V₂
Pressure ↑ → Volume ↓
Temperature
Temperature: A measure of the average kinetic energy of molecules.
Internal Energy
Internal Energy: Total microscopic energy of molecules in a substance.
Heat
Heat: Energy transferred because of a temperature difference.
Specific Heat
Specific Heat: The amount of heat required to raise the temperature of 1 kg of a substance by 1°C.
Heat equation: Q = cmΔT
Heat Transfer
Three mechanisms:
- Conduction: Heat transfer by direct contact of particles
- Convection: Heat transfer by motion of fluids
- Radiation: Heat transfer by electromagnetic waves (requires no medium)
Phase Changes
During phase change, temperature remains constant.
Types:
- Melting: solid to liquid
- Freezing: liquid to solid
- Evaporation: liquid to gas
- Condensation: gas to liquid
- Sublimation: solid to gas
Latent Heat
Latent Heat: Energy absorbed or released during a phase change without temperature change.
Exam Strategy (Physics)
- Identify what quantity the problem asks for
- Identify the concept (spring, pressure, energy, gas, etc.)
- Choose the matching formula