RegentsLab

Physics Regents Review Sheet

Physics is patterns. Every problem is a specific case of a general rule — learn the rules, all the specifics fall out.

Practice Physics freeReference & formulas

Big ideas

Kinematics

Describing motion without asking why. Position, velocity, acceleration.

Definitions

v = d/t,\ a = \Delta v / t

Velocity = displacement/time (with direction). Acceleration = velocity change/time.

Example: Speeds up 0 → 20 m/s in 4 s → a = 20/4 = 5 m/s²
Kinematic equation

v_f = v_i + at

Final velocity = initial + (accel × time). All variables scalar magnitudes here.

Example: Start at 10 m/s, a = 3 m/s², t = 4 s → v_f = 10 + 12 = 22 m/s
Position equation

d = v_i t + \tfrac{1}{2}at^2

Distance covered when accelerating.

Example: Start at rest, a = 2 m/s², t = 5 s → d = 0 + ½(2)(25) = 25 m
Free fall

Only gravity acts. a = g = 9.8 m/s² downward. Same for all masses (in vacuum).

Example: Drop object, how fast after 2 s? → v = 9.8 × 2 ≈ 19.6 m/s downward

Trap: Speed vs velocity. Regents will ask about direction, and 'moving in a circle' has changing velocity but constant speed.

Tip: For projectiles: horizontal velocity CONSTANT, vertical follows free fall. Treat them independently.

Forces & Newton's laws

Three laws that cover everything from planets to pushing a shopping cart.

First (inertia)

Object stays at rest / stays in motion at constant velocity, UNLESS net force acts.

Example: Car stops suddenly, you fly forward. Why? → Your body's inertia — Newton's 1st
Second

F = ma

Net force = mass × acceleration. Bigger mass → less accel for same force.

Example: 10 N pushing a 2 kg object → a = F/m = 5 m/s²
Third

Every force has an equal-and-opposite reaction force. On a DIFFERENT object.

Example: You push a wall. Wall pushes back? → Yes — that's why you don't fall through
Weight vs mass

W = mg

Mass is stuff (kg). Weight is gravity's pull on it (N). g = 9.8 m/s² on Earth.

Example: 60 kg person on Earth → W = 60 × 9.8 = 588 N

Trap: The reaction force in Newton's 3rd acts on a DIFFERENT object. You push the wall, wall pushes YOU (not itself).

Tip: Free-body diagram: draw the object as a dot, all forces as arrows OUT from it. Sum them for net force.

Energy, work, power

Energy is the ability to do work. Comes in kinetic (motion), potential (position), and many other forms.

Work

W = Fd\cos\theta

Force through a distance. In the direction of force. Units: joules (J).

Example: Push with 10 N for 3 m in direction of motion → W = 30 J
Kinetic energy

KE = \tfrac{1}{2}mv^2

Energy of motion. Scales with SQUARE of velocity — double the speed, quadruple the KE.

Example: 2 kg at 3 m/s → KE = ½(2)(9) = 9 J
Potential energy

PE = mgh

Gravitational PE = weight × height. Relative to some reference (usually ground).

Example: 5 kg object at 4 m height → PE = 5(9.8)(4) = 196 J
Conservation of energy

Total energy stays constant in a closed system. PE at top = KE at bottom (no friction).

Example: Roller coaster starts at 20 m. Speed at bottom? → mgh = ½mv² → v = √(2gh) ≈ 19.8 m/s
Power

P = W/t

Rate of doing work. Units: watts (W) = J/s.

Example: Do 500 J of work in 5 s → P = 100 W

Trap: cos θ in the work formula — if force is perpendicular to motion, cos 90° = 0. NO work done.

Tip: Total mechanical energy KE + PE stays constant with only gravity acting. Great shortcut for pendulums, coasters, drops.

Momentum

Mass × velocity. Conserved in every collision (as long as no external force).

Momentum

p = mv

Vector — has direction. Units: kg·m/s.

Example: 3 kg at 4 m/s east → p = 12 kg·m/s east
Impulse

J = F\Delta t = \Delta p

Force × time. Equals change in momentum.

Example: 10 N over 2 s → Impulse = 20 N·s = change in momentum
Conservation

Total momentum before = total after (no outside force). Always applies to collisions & explosions.

Example: 2 kg at 5 m/s hits 3 kg at rest. They stick. Find v. → 10 = 5v → v = 2 m/s

Trap: Momentum is a VECTOR. Opposite directions get opposite signs.

Tip: Airbags/crumple zones/bending knees when landing: INCREASE the collision time to DECREASE the force. Same impulse, gentler force.

Waves, sound, & light

Waves transfer energy without transferring matter. Frequency and wavelength are inversely related for a given speed.

Wave equation

v = f\lambda

Wave speed = frequency × wavelength.

Example: 500 Hz sound in air (v = 340 m/s) → λ = 340/500 = 0.68 m
Transverse vs longitudinal

Transverse: oscillation ⊥ to propagation (light, ropes). Longitudinal: parallel (sound).

Example: Sound wave? → Longitudinal — air molecules oscillate along direction of travel
Reflection, refraction, diffraction

Reflection: bounces off. Refraction: bends entering new medium. Diffraction: bends around obstacles.

Example: Light in water appears bent? → Refraction
Doppler effect

Source moving TOWARD observer → higher pitch (compressed waves). Away → lower pitch.

Example: Ambulance approaching → passing you → Higher pitch → drops as it passes

Trap: The medium doesn't travel with the wave. Ocean waves move energy; the water goes up and down in place.

Tip: EM spectrum order (low to high frequency): radio → micro → IR → visible (ROYGBIV) → UV → X-ray → gamma.

Electricity & circuits

Charges push through wires when driven by voltage, resisted by resistance.

Ohm's law

V = IR

Voltage = current × resistance. V in volts, I in amps, R in ohms.

Example: 12 V across 4 Ω resistor → I = V/R = 3 A
Series

One path. Same current everywhere. Resistances ADD. Voltages add. If one breaks, all break.

Example: 10Ω and 20Ω in series → R_total = 30 Ω
Parallel

Multiple paths. Same voltage across each branch. 1/R_total = 1/R₁ + 1/R₂. Total resistance LOWER than smallest.

Example: 10Ω and 20Ω in parallel → 1/R = 1/10 + 1/20 = 3/20 → R = 20/3 Ω
Power

P = IV = I^2 R = V^2/R

Rate of energy delivered. Watts. Three forms of the same equation.

Example: 5 A through a 4 Ω resistor → P = 25 × 4 = 100 W

Trap: In parallel, more resistors = LESS total resistance (extra paths). Counter-intuitive at first.

Tip: Household outlets are parallel — that's why unplugging one lamp doesn't kill the whole house.

Modern physics

Where classical physics breaks and quantum shows up.

Photon energy

E = hf

Light is packets. Higher frequency → more energetic photons.

Example: Green (5×10¹⁴ Hz), red (4×10¹⁴ Hz) — which has more energy? → Green
Photoelectric effect

Light kicks electrons off metal — but only if frequency exceeds a threshold. Intensity doesn't matter for threshold.

Example: Increase intensity of red light on metal that requires blue. Any electrons? → No — frequency below threshold
Atomic energy levels

Electrons in ATOMS have discrete energies. Jumping from high level to low emits a photon; low to high absorbs.

Example: Electron falls from n=3 to n=2 in H → Emits a photon (energy difference)
Mass-energy

E = mc^2

Mass and energy are interchangeable. c = 3×10⁸ m/s. Small mass → HUGE energy.

Example: 1 g converted to energy → ≈ 9×10¹³ J (whole city's daily power)

Trap: In the photoelectric effect: intensity affects NUMBER of electrons but not their energy. Frequency affects their energy.

Tip: The physics reference table has energy levels of H and Hg. Emission line questions are direct lookups.

Frequently asked questions

How should I study for the Physics Regents?

Work real past-exam questions by topic, review this one-page summary of the must-know concepts, and read the worked solution every time you miss one. The exam reuses the same ideas year after year.

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