Physics & engineering
AC real, reactive and apparent power
AC real, reactive and apparent power: Apparent power is RMS voltage × RMS current, multiplied by √3 for balanced three phase with line-to-line voltage.
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Physics & engineering
Choose a tool. The method, example and assumptions are included.
Physics & engineering
Fluid pressure from liquid head
Fluid pressure from liquid head using clearly labeled inputs, with the formula, a worked example and practical limits explained.
Physics & engineering
Gravitational potential energy
Gravitational potential energy using clearly labeled inputs, with the formula, a worked example and practical limits explained.
Physics & engineering
Hooke’s law spring force and energy
Hooke’s law spring force and energy: Within the linear elastic range, restoring force = −k × displacement and stored energy = ½ × k × displacement².
Physics & engineering
Ideal lever effort force
Ideal lever effort force: Balance moments about the pivot: effort force × effort arm = load force × load arm.
Physics & engineering
Kinetic energy
Kinetic energy using clearly labeled inputs, with the formula, a worked example and practical limits explained.
Physics & engineering
LC resonant frequency
LC resonant frequency: For an ideal lumped LC circuit, resonant frequency = 1 / (2π√(L × C)), with L in henries and C in farads.
Physics & engineering
Linear momentum
Linear momentum using clearly labeled inputs, with the formula, a worked example and practical limits explained.
Physics & engineering
Pipe flow velocity
Pipe flow velocity using clearly labeled inputs, with the formula, a worked example and practical limits explained.
Physics & engineering
Pipe internal capacity
Pipe internal capacity: Treat the internal bore as a cylinder: volume = π × (internal diameter / 2)² × length.
Physics & engineering
Pipe Reynolds number
Pipe Reynolds number using clearly labeled inputs, with the formula, a worked example and practical limits explained.
Physics & engineering
Two-solution concentration blend
Two-solution concentration blend: Solve low-volume + high-volume = final volume and low-concentration × low-volume + high-concentration × high-volume = target-concentration × final volume.
Physics & engineering
Ideal projectile horizontal range
Ideal projectile horizontal range: For equal launch and landing heights without drag, horizontal range = v² sin(2θ)/g.
Physics & engineering
Free-fall time from rest
Free-fall time from rest: For a body released from rest with constant gravity and no drag, fall time = √(2h/g).
Physics & engineering
Centripetal force
Centripetal force: The inward force needed for uniform circular motion is F = mv²/r.
Physics & engineering
Angular velocity from rotation rate
Angular velocity from rotation rate: Angular velocity in radians/second = RPM × 2π/60.
Physics & engineering
Torque from force and angle
Torque from force and angle: Torque magnitude = radius × force × |sin(angle between radius and force)|, in newton-metres.
Physics & engineering
Impulse and momentum change
Impulse and momentum change: Impulse = average net force × duration.
Physics & engineering
Archimedes buoyant force
Archimedes buoyant force: Buoyant force = fluid density × displaced volume × gravitational acceleration, directed upward in a static fluid.
Physics & engineering
Hydrostatic gauge pressure
Hydrostatic gauge pressure: Gauge pressure increase below a static fluid surface is ρgh.
Physics & engineering
Ideal gas pressure
Ideal gas pressure: Ideal gas pressure P = nRT/V, using R = 8.31446261815324 J/(mol·K).
Physics & engineering
Sensible heat energy
Sensible heat energy: Heat energy Q = mass × specific heat capacity × temperature change.
Physics & engineering
Latent heat for a phase change
Latent heat for a phase change: Energy for a phase change at the transition temperature is Q = mass × specific latent heat.
Physics & engineering
Linear thermal expansion
Linear thermal expansion: Change in length ΔL = original length × linear expansion coefficient × temperature change.
Physics & engineering
Steady thermal conduction through a slab
Steady thermal conduction through a slab: Heat transfer rate = conductivity × area × temperature difference / thickness for one-dimensional steady conduction.
Physics & engineering
Carnot thermal efficiency limit
Carnot thermal efficiency limit: Maximum reversible heat-engine efficiency = (1−cold temperature/hot temperature) × 100, with absolute temperatures.
Physics & engineering
Wave propagation speed
Wave propagation speed: Wave speed = frequency × wavelength.
Physics & engineering
Thin lens image distance
Thin lens image distance: For the real-is-positive thin-lens convention, 1/f = 1/object distance + 1/image distance.
Physics & engineering
Snell’s law refraction angle
Snell’s law refraction angle: n₁sin θ₁ = n₂sin θ₂.
Physics & engineering
Sound intensity level
Sound intensity level: Sound intensity level = 10 log₁₀(intensity/reference intensity), in decibels.
Physics & engineering
Combine independent sound levels
Combine independent sound levels: For uncorrelated sources with the same reference, combined level = 10 log₁₀(10^(L₁/10)+10^(L₂/10)).
Physics & engineering
Coulomb electrostatic force
Coulomb electrostatic force: Signed interaction F = k q₁q₂/r² with k ≈ 8.9875517923×10⁹ N·m²/C².
Physics & engineering
Electric field from a point charge
Electric field from a point charge: Radial electric field = kq/r² with k ≈ 8.9875517923×10⁹ N·m²/C².
Physics & engineering
Uniform wire resistance
Uniform wire resistance: Resistance R = resistivity × length / cross-section area, converting mm² to m².
Physics & engineering
Energy stored in an inductor
Energy stored in an inductor: Stored magnetic energy = ½ × inductance × current² for a linear inductor.
Physics & engineering
Ideal transformer secondary voltage
Ideal transformer secondary voltage: Ideal secondary voltage = primary voltage × secondary turns / primary turns.