Physics Formulas and Concepts: A Quick Reference

Posted on Feb 4, 2025 in Physics

Physics Formulas and Concepts

V = Δt / Δs DT → VT, use slopes VT → DT, use area VT → AT, use slopes AT → VT, use area S(t) = S∘ + VΔt + ½aΔt² ∆s = ½(Vi + Vf)∆t ∆s = Vf∆t – ½aΔt² Vf² = Vi² – Vi² = 2a∆s Note: if velocity is doubled the breaking distance will quadruple.

3[S]+4[W] = √3² + 4²[ tan⁻¹(4/3) W) = 5[S 53° W] 13[N 27° E] = 13sin27° [E] + 13 cos 27°[N] = 5.9[E] + 11.55 [N] sine gives [E] / [W] cosine [N] / [S] Note: doing tan⁻¹( ), it is x-component (E/W) over the y- component (N/S) (only if [N_E]→[E_N] convert before flipping [E 35° N] ) = [N 55° E]) Note: if the velocities relativity is the opposite (Vcs→ Vsc) , take the opposite directions and keep the same numbers

Velocity

  • Air Velocity→ Velocity of the object relative to the air (wind)
  • Ground Velocity→ Velocity of the object relative to the ground
  • Wind Velocity→ Velocity of wind relative to the ground

Note: Projectile Motion sometimes find horizontal and vertical components. n ao

Newton’s Laws

  • Newton’s 1st Law → Mass vs weight
  • Inertia → Is the tendency of the object to resist the change in motion, unless acted upon by an unbalanced force [If initially in motion it wants be maintain the same velocity], [If initially at rest , it wants to remain at the rest].
  • Newton’s 2nd Law → The net unbalanced force is the product of masses and acceleration F= ma Fg= mg
  • Newton’s 3rd Law of Reaction Force → Any Force has the same amount of force going back on it.

Note: If static friction is larger than applied force, that is the max and friction will be equal to the magnitude of the applied force because friction cannot move an object and if static friction is smaller than applied force, it is not able to stop the object, making it become in motion therefore the kinetic friction will be used.

Note: Has an upward acceleration (accelerating upward or decelerating down) → feel heavier → FN = m(g + a), has a downward acceleration (accelerating down or decelerating up) → feel lighter → FN = m(g – a)

Thermodynamics

  • Temperature → average potential energy of particles ∞ to the speed of particles.
  • Internal Energy (I) → sum of all kinetic energies of the particles.
  • Heat (Q) → transfer of thermal energy from one object to another.

Note: bigger ΔI ≠ bigger Q because you need to take the masses into account.

  • Conduction → touching particles to transfer energy.
  • Convection → Lower density rises, higher density sinks.
  • Radiation → receiving thermal energy from electromagnetic waves (lights, microwaves).
  • Specific Heat (c) → energy required to raise 1kg of substance by 1°C Q = mcΔt Δt = Q/P
  • Latent Heat (L) → energy required to turn 1kg of substance from one phase to another Q = mL

E = (Solar Insulation w/m²) (area m²) (efficiency)

Note: 1kwh is the amount of energy consumed by a 1kw device for one hour.

Energy and Work

  • Work Done → W = FΔscosΘ Wnet = W1 + W2 +…. or Wnet = Fnet∆s
  • Kinetic Energy → Ek = ½mv²
  • Potential Energy → Eg = mg∆h

Note: gravitational potential energy is the work done by gravity when the object moves from its current location to its reference location.

  • P = w/∆t
  • Mechanical Power → 1hp = 746W
  • 1cal = 4186J
  • Conservative Force → does not care about the path (gravity)
  • Non-Conservative Force → cares about the path (friction, resistance)

Nuclear Physics

  • Fusion → small to big (high temperature and pressure core, all starts including sun)
  • Fission → big to small (high temperature produced, nuclear power plants, very long half-life)
  • Gamma Decay → release of energy of an electron from higher energy level to lower energy level
  • Alpha Decay → atom in a somewhat unstable state will have a tendency to return to stability, emitting a helium nucleus. X → n-4/z-2 X + 4/2 He
  • Beta Decay – → emitting an electron 207/82 Pb → β- + 207/83 Bi

Beta Decay + → emitting a positron 207/82 Pb → β+ + 207/81 Tl

  • Energy → J, kJ, kwh
  • Power → w → kw

Work-Kinetic Energy Theorem → Wnet = ∆Ek

Conservation of Energy → Ek1 + Eg1 + Wnet = Ek2 + Eg2

Waves

  • Wave → result of a oscillation, transfer of energy
  • Transverse Wave → oscillation of particle is perpendicular to the motion of the wave (ocean waves)
  • Longitudinal Wave → oscillation of particle is parallel to the motion of the wave (sound waves)
  • Nodes → particles don’t move (at equilibrium)
  • Anti-Node → maximum amplitude

Density ↑, Speed ↑

V = λf f = 1/t Hz = 1/s Vs = 331.6 + 0.606T*C M = 10log (I/ I∘) I = 10M/10 I∘ Note: the closer compressions create higher frequencies and further compressions create lower frequencies.

  • String → L = nλ/ 2 → λ = 2L/n
  • Closed Air-Column → λ = 4L/ 2n – 1
  • Open Air-Column → λ = 2L/n

f∘ = (V +- Vo/ V +- Vs) fs Note: adding in denominator causes lower number and lower frequency, adding in numerator causes higher number and higher frequency.

fb = | f2 – f1 | Note: constructive and destructive interference creates a beat

Mach Speed → mach 2 = 2 times the speed of sound

Electricity and Magnetism

  • Cell → a single unit of a device to convert chemical energy into electrical energy
  • Battery → collection of cells

A = c/s V = J/c

  • Current → movement of protons
  • Electron Flow → movement of electrons
  • Electrode → anode (positive) and cathode (negative)

Note: 1mAh is the amount of charge in a battery that will support a 1mA current for 1 hour

Circuits

  • Series Circuit → VT = V1 + V2 +… RT = R1 + R2 +… IT = I1 = I2… V = IR P = VI P = V²/ R
  • Parallel Circuits → VT = V1 = V2… 1/RT = 1/R1 + 1/R2 +… I = I1 + I2+…

Internal Resistance → ε – Ir = IR

  • Electric Motor Force (EMF) → electrical potential produced by a cell
  • Terminal Voltage → electrical potential after internal resistance
  • Transformers → device that changes the voltage of incoming current without changing the power (step-up or step-down) Vp/ Vs = Np/ Ns
  • Magnetic Field → comes out of the north end and goes to the south end

Note: The geographic North Pole is the magnetic South Pole, and the geographic South Pole is the magnetic North Pole (needle points to direction of magnetic field)

Rules

  • Rule #1 → Thumb: direction of current, Fingers: direction of magnetic field, Palm: pushes in direction of the force

Note: if the particle is negative, the current is going in the opposite direction

Note: a steady current creates a magnetic field and a change in magnetic field induces a current.

  • Rule #2 → Thumb: direction of current, Fingers: curl in direction of magnetic field
  • Rule #3 → Thumb: points to North, Fingers: in direction of current (solenoid)

Lenz’s Law → when a magnet is moving, there is a changing magnetic field. The induced current creates an electromagnet in such a way that opposes the motion of the original magnet.

Math

Quadratic Formula →x = [-b ± √(b2 – 4ac)]/2a