IIT JAM Physics cheat sheet

Physics (JAM Physics test paper)

• Vector calculus: div(grad f) = ∇²f; curl(grad f) = 0; div(curl A) = 0. Stokes' theorem ∮A·dl = ∫(∇×A)·dS and divergence theorem ∮A·dS = ∫(∇·A)dV.

• Newtonian gravity and electrostatics share the same inverse-square form: F = Gm₁m₂/r² and F = q₁q₂/(4πε₀r²); Gauss's law analogies transfer directly between them.

• Rotational dynamics: τ = Iα, L = Iω; for a rigid body rolling without slipping, v = ωR and total KE = ½mv² + ½Iω². Parallel-axis theorem I = I_cm + Md².

• SHM: for a spring, ω = √(k/m) and T = 2π√(m/k); for a simple pendulum, T = 2π√(L/g); for a physical pendulum, T = 2π√(I/mgd). Damping: x = A e^(−bt/2m) cos(ω′t).

• Waves: v = √(T/μ) on a string; standing-wave frequencies on a string fixed at both ends are f_n = nv/(2L); for a pipe open at both ends, f_n = nv/(2L); for a pipe closed at one end, f_n = (2n−1)v/(4L).

• Doppler effect: f′ = f (v ± v_o)/(v ∓ v_s), where the upper sign in the numerator applies when the observer moves toward the source, and the upper sign in the denominator applies when the source moves away from the observer.

• Thermodynamics: ΔU = Q − W; for an ideal gas, C_p − C_v = R and γ = C_p/C_v; adiabatic relation PV^γ = constant; Carnot efficiency η = 1 − T_c/T_h.

• Special relativity: γ = 1/√(1 − v²/c²); time dilation Δt = γΔt₀; length contraction L = L₀/γ; relativistic energy E² = (pc)² + (m₀c²)² and KE = (γ−1)m₀c².