PHYS 101 – Equations for Final Exam Motion and Vectors: Speed = d/Δt v = Δd/Δt (give direction) a = Δv/Δt d = ½ at2

(starting from rest) v13 = v12 + v23 (Relative Velocity) Forces: ΣF = Fnet = ma (Newton 2nd Law) F21 = - F12 (Newton 3rd Law) w = mg (Weight) Work and Energy: Work = F•d Power = Work/Δt Etot = KE + PE KE = ½ mv2 PEgrav = mgh W = ΔKE Momentum and Impulse: Momentum (p) = mv Impulse = Fav Δt Δp = External Impulse Rotational Motion: ω = Δθ/Δt vt = 2πRω Torque (τ) = Force x r⊥(r⊥ is lever arm) L = Iω (rigid body) ΔL/Δt = τext

Equilibrium: Fnet = ΣF = 0; τnet = Στ = 0 Fcent = mv2/r Gravity and Projectiles: Fgrav = (Gm1m2)/d2 Properties of Matter: Pressure = F/A mass density = m/V weight density = mg/V Liquid pressure = weight density x depth P1V1 = P2V2 Heat: Heat Added = Increase in Internal E + Work

Sound: f = 1/T ; T = 1/f vw = f x λ Electricity and Magnetism: Electric Force: Fe = kq1q2/r2 Electric Field: E = Fe/q Electric Potential: V = Electric PE/ q Ohm’s Law: V = IR Power: P = IV or P = I2R Transformers: V1/N1=V2/N2 Faraday’s Law: Induced voltage in a coil is proportional to the product of its number of loops, the cross-sectional area of each loop, and the rate at which the magnetic field changes in those loops Maxwell’s Counterpart to Faraday’s Law: A magnetic field is induced in any region of space in which an electric field is changing with time. Right hand rule (version 1): If thumb points in direction of current, fingers on right hand curl in direction of the magnetic field around a wire. Right hand rule (version 2): If fingers point in direction of current and magnetic field points out of the palm, then thumb points in direction of the magnetic force exerted on a positively-charged particle, and opposite direction for magnetic force exerted on a negatively-charged particle. Light and Modern Physics: Law of reflection: θI = θR EM waves (light) in vacuum: λ x f = c Planck energy of photons: E = h x f de Broglie wavelength: λ = h/(mv) Mass-Energy equivalence: E = mc2

Special Relativity: Time Dilation: t = t0 /√(1-v2/c2) Length Contraction: L = L0√(1-v2/c2)

Constants: Index of Refraction Conversion Factors k = 9.0 x 109 N m2/C2 vacuum: n = 1.00 1 km = 103 m Charge of electron: -1.602 x 10-19 C air: n = 1.0003 1 m = 102 cm Charge of proton: +1.602 x 10-19 C water: n = 1.33 1 cm = 101 mm Mass of electron: 9.1 x 10-31 kg glass: n = 1.5 1 nm = 10-9 m Mass of proton: 1.67 x 10-27 kg diamond: n = 2.42 Speed of Light in vacuum (c): 3.0 x 108 m/s Speed of Sound in air: 340 m/s Planck’s constant (h) = 6.6 x 10-34 J-s G = 6.67 x 10-11 N m2/kg2 QUANTITY SYMBOL UNIT OR VALUE COMMENTS Mass m kg Length or distance d m Time t s Velocity v m/s Magnitude is speed Acceleration a m/s2 Force F N N=kg-m/s2 Accel. of gravity g or g 10 m/s2 or 10 N/kg Work W J J = Nm Kinetic Energy KE J Potential Energy PE J Mechanical Energy E J E = KE + PE Power P W W = J/s Linear Momentum p kg-m/s Impulse I N-s Angular Position θ rev Other units: degrees, radians Angular Velocity ω rev/s Other units: rev/min (RPM) Torque τ N-m Rotational Inertia I kg-m2

Angular Momentum L kg-m2/s Volume V m3 or liters 1 liter = 10-3 m3

Density ρ kg/m3 ρ = M/V Pressure P Pa 1 Pa = 1 N/m2; Other unit: PSI Temperature T K or °C Heat Q J Period T s Frequency f Hz Hz = 1/s Wavelength λ m Wave velocity v or vw m/s Amplitude A m, Pa, etc. Charge q C Coulomb Potential Energy PE J Electric Potential V V Volts, Voltage Resistance R Ω Ω Current I A Amperes