Physiworld · NGSS physics formula sheet · www.physiworld.com/ngss-physics/formula-sheet/
NGSS physics standards map NGSS-aligned physicsFormula sheet
The key relationships that the high-school physical science and astronomy performance expectations use, each tagged with its expectation code, with what each symbol means and its unit. Each equation links the Physiworld lesson that teaches it; lessons open with a free account. The revision notes explain each topic with worked examples.
NGSS has no official equation sheet. The standards set performance expectations, not a list of equations, and your state or district test may give its own reference sheet. These are the relationships the expectations are built on.
HS-PS2 · Forces and interactions
| Equation | What it says, symbols and units | Lesson |
|---|---|---|
F = ma | A resultant force accelerates a mass, in the direction of the force.
| Dynamics 1 · Newton’s Second Law |
W = mg | Weight is the gravitational force on a mass; on Earth g is about 9.8 N/kg.
| Gravity 1 · Mass & Weight |
p = mv | Momentum is mass times velocity, and it has a direction.
| Dynamics 2 · Momentum |
total momentum before = total momentum after | In a collision or explosion with no outside force, the total momentum does not change. | Dynamics 2 · Conservation of Momentum |
impulse = FΔt = Δ(mv) | A force acting for a time changes the momentum by that amount.
| Dynamics 2 · Impulse |
Fg = Gm1m2r2 | Every two masses attract; double the distance and the force is a quarter. G = 6.67 × 10⁻¹¹ N m²/kg².
| Gravity 2 · Gravity and Distance |
Fe = kq1q2r2 | Two charges attract or repel with an inverse-square force. k = 8.99 × 10⁹ N m²/C².
| Electricity 4 · The Fading Field |
HS-PS3 · Energy
| Equation | What it says, symbols and units | Lesson |
|---|---|---|
Ek = ½mv2 | Energy of a moving object; double the speed and the kinetic energy is four times as big.
| Dynamics 3 · Kinetic Energy |
ΔEp = mgΔh | Energy gained by a mass lifted through a height, near the Earth's surface.
| Dynamics 3 · Energy Conservation |
Us = ½kx2 | Energy stored in a stretched or compressed spring.
| Dynamics 6 · Elastic Potential Energy |
W = Fd = ΔE | The work a force does is the energy it transfers.
| Dynamics 3 · Work Done |
total energy before = total energy after | In a closed system energy is never made or destroyed, only transferred between stores. | Dynamics 3 · Energy Conservation |
P = Wt = ΔEt | Power is how fast work is done or energy is transferred; 1 W is 1 J each second.
| Dynamics 3 · Power |
efficiency = useful energy outputtotal energy input (× 100%) | The share of the input that ends up useful; the same with useful power output over total power input. Never more than 100%.
| Dynamics 3 · Power |
V = IR | Potential difference is current times resistance.
| Electricity 3 · Resistance |
P = IV | Electrical power is current times potential difference.
| Electricity 5 · Power & Fuses |
Q = mcΔT | Thermal energy needed to change the temperature of a mass; heat flows until both objects reach the same temperature.
| Thermal 1 · Specific Heat Capacity |
HS-PS4 · Waves
| Equation | What it says, symbols and units | Lesson |
|---|---|---|
v = fλ | Wave speed is frequency times wavelength, for every kind of wave.
| Waves 1 · Wave Speed |
T = 1f | The period is the time for one complete wave; it is one over the frequency.
| Waves 4 · Frequency & Wavelength |
c = fλ | Light and all electromagnetic waves: c = 3.00 × 10⁸ m/s in a vacuum.
| Waves 6 · The EM Spectrum |
E = hf | Light comes in photons; higher frequency means more energy per photon. h = 6.63 × 10⁻³⁴ J s.
| Waves 9 · Wave or Particle? |
HS-PS1-8 · Nuclear processes
| Equation | What it says, symbols and units | Lesson |
|---|---|---|
E = mc2 | In fission and fusion a little mass disappears and a lot of energy is released.
| Nuclear 3 · Mass and Energy |
N = N0(½)t/t½ | The undecayed nuclei halve every half-life.
| Nuclear 2 · Half-Life |
HS-ESS1 · Earth and the universe
| Equation | What it says, symbols and units | Lesson |
|---|---|---|
T2 ∝ r3 | For bodies orbiting the same star or planet, the further out, the longer the year.
| Gravity 3 · Kepler’s Third Law |
v = √(GMr) | Speed of a circular orbit; it does not depend on the mass of the orbiting body.
| Gravity 2 · Orbital Speed |
v = H0d | Galaxies recede at a speed proportional to their distance: the evidence for an expanding Universe.
| Space 6 · Hubble’s Law |
Written in Physiworld's own words. Expectation codes are the NGSS's.
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