ILTS Science: Physics (243) cheat sheet

A scientific law describes a consistent relationship, often mathematically; a theory explains why that relationship occurs and is supported by multiple lines of evidence.

A testable hypothesis must be falsifiable; predictions specify measurable outcomes that could contradict the claim.

The independent variable is manipulated, the dependent variable is measured, and controlled variables are held constant to prevent confounding.

Random selection supports generalization to a population; random assignment to treatments supports causal inference.

Accuracy is closeness to the true value; precision is closeness among repeated measurements; random error affects precision, while systematic error affects accuracy.

Uncertainty rules: for addition or subtraction add absolute uncertainties; for multiplication or division add relative uncertainties; percent error = |measured − accepted| / accepted × 100%.

Standard deviation quantifies spread about the mean; a smaller standard deviation indicates measurements clustered more tightly around the mean.

Correlation does not establish causation; a controlled experiment or strong quasi-experimental design is needed to support causal claims.

Constant-acceleration kinematics: v = v0 + at; Δx = v0t + ½at²; v² = v0² + 2aΔx.

Newton's second law: ΣF = ma; net force and acceleration are parallel, and mass measures resistance to acceleration.

Newton's third law: forces occur in equal-and-opposite pairs acting on different objects, so they do not cancel within one object's free-body diagram.

Projectile motion separates into constant horizontal velocity and vertical acceleration g; time of flight is determined by vertical motion.

Circular motion at constant speed has centripetal acceleration ac = v²/r directed toward the center; no outward centrifugal force exists in an inertial frame.

Work W = Fd cosθ; kinetic energy KE = ½mv²; gravitational PE = mgh; spring PE = ½kx²; nonconservative work equals change in total mechanical energy.

Impulse J = FΔt = Δp; total momentum is conserved when net external impulse is zero, as in collisions and explosions.

Static equilibrium requires ΣF = 0 and Στ = 0; torque τ = rF sinθ, with θ the angle between lever arm and force.

Coulomb's law: F = k|q1q2|/r²; electric field E = F/q, and for a point charge E = kq/r².

Ohm's law V = IR; resistance R = ρL/A, so longer or thinner wires have greater resistance.

Series: same current, voltages add, Req = R1 + R2 + ...; parallel: same voltage, currents add, 1/Req = 1/R1 + 1/R2 + ...

Electric power P = IV = I²R = V²/R; energy consumed in kWh equals power in kW times time in hours.

Capacitance C = Q/V; parallel plates C = ε0A/d; capacitors in parallel add, in series use reciprocal sum; stored energy U = ½CV².

Magnetic force on moving charge F = qvB sinθ and on current-carrying wire F = ILB sinθ; direction follows the right-hand rule.

Faraday's law: induced emf ε = −NΔΦ/Δt; Lenz's law says induced current opposes the flux change that caused it.

Kirchhoff's rules: junction rule conserves charge (ΣIin = ΣIout); loop rule conserves energy (ΣΔV = 0 around a closed loop).

Wave relation v = fλ; period T = 1/f; wave speed is determined by the medium, while frequency is set by the source.

Mechanical waves require a medium; electromagnetic waves propagate in vacuum at c ≈ 3.00 × 10⁸ m/s and are transverse.

Constructive interference occurs when path difference is mλ; destructive interference when path difference is (m + ½)λ.

Standing waves have nodes at fixed points and antinodes halfway between; boundary conditions determine allowed wavelengths.

Reflection follows θi = θr; refraction follows Snell's law n1 sinθ1 = n2 sinθ2, with index n = c/v.

Total internal reflection occurs only from higher to lower index when θ exceeds critical angle θc, where sinθc = n2/n1.

Thin lens/mirror equation 1/f = 1/do + 1/di and magnification m = −di/do; real images can be projected, virtual images cannot.

Double-slit maxima occur at d sinθ = mλ; single-slit minima at a sinθ = mλ; polarization confirms light's transverse nature.

Temperature conversion: T(K) = T(°C) + 273.15; T(°F) = (9/5)T(°C) + 32; absolute zero is 0 K.

Heat transfer Q = mcΔT for temperature change and Q = mL for phase change at constant temperature.

First law of thermodynamics: ΔU = Q − W, where Q is heat added to the system and W is work done by the system.

Ideal gas law PV = nRT; at constant n, P1V1/T1 = P2V2/T2 with temperatures in kelvin.

Work done by a gas is the area under the PV curve; isobaric W = PΔV, isothermal W = nRT ln(Vf/Vi), adiabatic Q = 0.

Heat engine efficiency η = W/Qh = 1 − Qc/Qh; Carnot maximum ηC = 1 − Tc/Th using absolute temperatures.

Second law: entropy of an isolated system never decreases; natural processes are irreversible and require energy dispersal.

Heat transfer modes: conduction through direct contact, convection by fluid motion, radiation by electromagnetic waves; Stefan-Boltzmann P = εσAT⁴.

Photon energy E = hf = hc/λ; photoelectric emission requires f > f0, where work function φ = hf0.

Maximum photoelectron kinetic energy Kmax = hf − φ = eVstop; intensity changes current, not stopping voltage.

Atomic spectra arise from quantized energy levels; emitted or absorbed photon energy equals ΔE = hf.

de Broglie wavelength λ = h/p; matter waves explain electron diffraction and quantization in confined systems.

Hydrogen Bohr levels En = −13.6 eV/n²; transitions to n = 1 produce Lyman series, to n = 2 produce Balmer series.

Radioactive decay: N = N0(1/2)^(t/T½); activity decreases by half each half-life; alpha, beta, gamma differ in charge and penetration.

Mass-energy equivalence E = mc²; nuclear binding energy equals mass defect times c², and fusion releases energy for light nuclei.

Special relativity: moving clocks run slow (Δt = γΔt0), lengths contract along motion (L = L0/γ), and c is invariant for all inertial observers.