Physics Level 4 cheat sheet

Dimensional analysis check: every term in an equation must reduce to the same base units (kg, m, s, A, K, mol, cd); a mismatch signals an algebra error before any numbers are substituted.

Standard prefixes: p = 1e-12, n = 1e-9, micro = 1e-6, m = 1e-3, k = 1e3, M = 1e6, G = 1e9; convert all data to SI base units before calculating.

Kinematics at constant acceleration: v = u + at, s = ut + 0.5at^2, v^2 = u^2 + 2as; choose the equation containing the three knowns plus the one unknown.

Newton's second law is a vector relation: resolve forces into perpendicular components, sum each separately, and set F_net = ma along each axis independently.

Momentum is conserved in all collisions; kinetic energy is conserved only in elastic ones. Use m1u1 + m2u2 = m1v1 + m2v2 first, then test KE if elasticity is claimed.

Circular motion: centripetal acceleration a = v^2/r = omega^2 r, directed toward the centre; the centripetal force is the resultant of real forces, never an extra force.

Energy conservation route: identify initial and final stores (kinetic, gravitational mgh, elastic 0.5kx^2), account for work done against friction, and equate.

Waves and optics: v = f lambda; for a single slit first minimum sin(theta) = lambda/a, for a diffraction grating maxima d sin(theta) = n lambda.

Electricity: Ohm's law V = IR holds for ohmic conductors at constant temperature; series resistances add, parallel conductances add, and power P = VI = I^2R = V^2/R.

Significant figures and units carry marks: report the answer to the least precise input, attach the unit, and state direction for any vector quantity.

Resolution is the smallest scale division of an instrument; the reading uncertainty is normally taken as half a division for analogue scales and the last displayed digit for digital meters.

Percentage uncertainty of a single reading = (absolute uncertainty / measured value) x 100; for repeated readings use the half-range of the spread or the standard deviation of the mean.

Combining uncertainties: for sums and differences add absolute uncertainties; for products and quotients add percentage uncertainties; for a power n multiply the percentage uncertainty by n.

Uncertainty in a gradient: plot error bars and a best-fit line, then draw the steepest and shallowest lines consistent with the bars; half the difference of their gradients is the gradient uncertainty.

To test a relationship such as T = 2 pi sqrt(L/g), plot T^2 against L; a straight line through the origin confirms proportionality and the gradient gives 4 pi^2/g.

Systematic errors shift all readings in one direction (zero error, calibration drift) and are not reduced by averaging; random errors scatter both ways and are reduced by repeats.

Common systematic pitfalls: parallax when reading a meniscus or ruler, uncalibrated balances, timing reaction delay in stopwatch work, and neglecting the mass of a spring or pulley.

Precision describes the spread of repeats; accuracy describes closeness to the true value. A precise set can still be inaccurate if a systematic error is present.

Safety and control: identify the independent, dependent and controlled variables, clamp apparatus to avoid toppling, keep liquids away from electrical equipment, and use a heatproof mat with hot masses.