Maths Equations Flashcards
What is the formula for force?
Force (N) = mass (kg) × acceleration (m/s²)
F = ma
How is weight calculated?
Weight (N) = mass (kg) × gravitational field strength (9.81 m/s²)
W = mg
What is the formula for moment?
Moment (Nm) = force (N) × perpendicular distance from pivot (m)
M = Fd
What does the principle of moments state?
Sum of clockwise moments = Sum of anticlockwise moments (for equilibrium)
This principle is crucial in mechanics.
How is pressure calculated?
Pressure (Pa) = force (N) / area (m²)
P = F / A
What is the formula for work done?
Work done (J) = force (N) × distance (m)
W = Fd
How is kinetic energy calculated?
Kinetic energy (J) = ½ × mass (kg) × velocity² (m/s)
KE = ½mv²
What is the formula for gravitational potential energy?
Gravitational potential energy (J) = mass × gravity × height
GPE = mgh
How is efficiency calculated?
Efficiency (%) = (useful energy output / total energy input) × 100
This measures how well energy is converted.
What is the formula for stress?
Stress (Pa) = force (N) / cross-sectional area (m²)
σ = F / A
How is strain defined?
Strain = extension / original length (no units)
ε = ΔL / L
What is Young’s Modulus?
Young’s Modulus (Pa) = stress / strain
E = σ / ε
How is density calculated?
Density (kg/m³) = mass (kg) / volume (m³)
ρ = m / V
What is Ohm’s Law?
Voltage (V) = current (A) × resistance (Ω)
V = IR
How is power calculated in electrical systems?
Power (W) = voltage × current
P = VI
What is the formula for energy in electrical systems?
Energy (J) = power × time (s)
E = Pt
What are the alternate power equations?
P = I²R or P = V² / R
These equations offer different ways to calculate power.
How is charge calculated?
Charge (C) = current (A) × time (s)
Q = It
What is the formula for specific heat capacity?
Energy = mass × specific heat capacity × temperature change
E = mcΔT
What does the ideal gas law state?
PV = nRT
This relates pressure, volume, temperature, and amount of gas.
What is the formula for angular velocity?
Angular velocity (rad/s) = angle (radians) / time
ω = θ / t
How is rotational kinetic energy calculated?
Rotational kinetic energy = ½ × moment of inertia × angular velocity²
KE_rot = ½Iω²
What is the formula for mechanical advantage?
Mechanical advantage (MA) = load / effort
This measures the efficiency of a machine.
How is velocity ratio calculated?
Velocity ratio (VR) = distance moved by effort / distance moved by load
This relates to the movement efficiency of machines.
What is the formula for efficiency in machines?
Efficiency = (MA / VR) × 100
This indicates how effectively a machine converts input to output.
