Formula Sheet

Key Concepts

Key Topics

• Motion

• Forces

• Momentum

• Hooke's Law

• Pressure

• Energy

• Work

• Power

• Boyle's Law

• Thermal Dynamics

• Wave Equations

• Snell's Law

• Electrical Concepts.

Formula Sheet

A compilation of essential physics formulas for quick reference.

Mechanics and Motion

Electrical Power

The rate at which electrical energy is transferred or converted.

Decay Types

• Alpha Decay (α): Emission of an alpha particle (2 protons, 2 neutrons).

• Beta Decay (β): Transformation of a neutron into a proton, emitting a beta particle.

• Gamma Decay (γ): Release of gamma radiation from a nucleus.

Equations of Motion

• Speed (v): v = ( \frac{d}{t} ) (Distance over Time)

• Velocity (v): v = ( \frac{\Delta x}{\Delta t} ) (Displacement over Time)

• Acceleration (a): a = ( \frac{\Delta v}{t} ) (Change in Velocity over Time)

Forces

• Resultant Force (ΣF): ΣF = Mass × Acceleration = ma

• Weight (W): W = Mass × Gravitational Constant = mg

Momentum Calculations

• Momentum (p): p = Mass × Velocity = mv

• Conservation of Momentum: Total momentum before = Total momentum after collision ( m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2 )

Energy and Work

Impulse

Impulse = Force × Time = Ft = ( \Delta p )

Moment

Moment = Force × Distance = Fd

Rotational Equilibrium

Resultant clockwise moment = Resultant anticlockwise moment

Hooke's Law

Spring Constant (k) = ( \frac{F}{x} ) (Force over Extension)

Pressure

• General Definition: Pressure (p) = ( \frac{F}{A} )

• Pressure in Liquids: p = Density × Gravitational Constant × Height (Depth) = ρgh

Energy Types

• Kinetic Energy (KE): KE = ( \frac{1}{2} mv^{2} )

• Gravitational Potential Energy (GPE): GPE = mgh

• Mechanical Energy: Total Energy = KE + GPE

Energy, Work, and Efficiency

Elastic Potential Energy (EPE)

EPE = ( \frac{1}{2} kx^{2} )

Work Done (W)

W = Fd = ( \Delta E )

Power (P)

P = ( \frac{W}{t} )

Efficiency

Efficiency = ( \frac{Useful Energy Output}{Total Input Energy} ) × 100%

Boyle's Law

p1V1 = p2V2 (Pressure-Volume relationship)

Thermal Dynamics

• Heat Capacity: Heat = mc( \Delta T )

• Specific Heat Capacity (c): c = ( \frac{\Delta E}{m \Delta T} )

Waves and Optics

Wave Equations

• Frequency = ( \frac{1}{T} ) (Time Period)

• Speed (v): v = Frequency × Wavelength = fλ

Snell's Law

Refractive Index (n) = ( \frac{sin(i)}{sin(r)} )

Critical Angle Calculation

n = ( \frac{1}{sin(c)} )

Electrical Concepts

• Current (I): I = ( \frac{Q}{t} )

• Potential Difference (Voltage): V = ( \frac{W}{Q} )

• Ohm's Law: R = ( \frac{V}{I} )

• Resistivity and Resistance: ( R = \rho \frac{l}{A} )

• Total Resistance in Circuits: R_T = R1 + R2 + ... + Rn

Circuit Analysis

Parallel Resistance

R_T = ( \frac{1}{R_1} + \frac{1}{R_2} + \ldots )^{-1}

Power Calculations

• Power (P): P = Voltage × Current = V × I

• Power Dissipated: P = I²R = ( \frac{V^2}{R} )

Transformers

Voltage ratio = ( \frac{N_s}{N_p} )

Decay Models

• Alpha Decay: zAX → z−2A−4Y + 2 4He

• Beta Decay: zAX → z+1AY + −1 0e + ν̅

• Gamma Decay: zAX → zAX + γ

Orbital Speed

Speed (v) = ( \frac{2πr}{T} )

Hubble's Law

Hubble's Law Equation: Speed (v) = H × Distance Where H = Hubble's Constant.