Final Exam Review
Physics 103 - Spring 98

Kinematics

• Position, velocity, acceleration (average and instantaneous)
• Velocity: v = v₀ + at
• Displacement: x = v₀t + at²/2
• v² = v₀² + 2ax
• a = g = 9.8 m/s² for objects near Earth's surface
• 1-D, 2-D and 3-D motions, vectors

Newton's Laws

• 1. Law of inertia (mass)
• 2. Law of force: F = ma
• 3. Law of action and reaction
• Normal forces (N)
• Friction forces: f = mN
• Force diagrams, pulleys

Energy

• Work: W = F·s
• Kinetic energy: KE = mv²/2
• Work-energy theorem: W = DKE
• Gravitational potential energy: PE = mgh
• Conservation of energy: E = KE + PE = constant (if W_NC = 0)
• Spring: F = -kx, PE = kx²/2
• Power: P = W/t = F·v

Collisions

• Momentum: p = mv
• Impulse: I = FDt = Dp
• Conservation of momentum: Sp = constant if F_ext = 0
• Elastic versus inelastic collisions

Rotations

• q = s/r, w = v/r, a = a/r
• Radians versus degrees (1 rad = 57.3º)
• Centripetal acceleration: a_r = v²/r
• Centripetal force: F = mv²/r
• Universal gravitation: F = Gm₁m₂/r²
• Kepler's Laws
• Torque: t = Fd (d is the moment arm)
• Equilibrium: SF = 0: St = 0
• Center of gravity
• Moment of inertia: I = Smr²
• t = Ia, KE = Iw²/2, etc.
• Angular momentum: L = Iw
• t = DL/Dt ==> L = constant if t_ext = 0

Fluids

• Elasticity, Young's modulus, Bulk modulus
• Density: r = M/V (mass per unit volume)
• Pressure: P = F/A (force per unit area)
• Variation with depth: P = P₀ + rgh
• Archimedes' principle, buoyancy
• Continuity equation: Av = constant
• Bernoulli's equation: P + rv²/2 + rgy = constant

Heat

• Temperature, units, conversions, etc.
• Thermal expansion: DL = aL₀DT
• Ideal gas: PV = nRT or PV = NkT
• Avogadro's number, moles, etc.
• Average molecular kinetic energy: E_av = 3NkT/2
• Heat: Q = mcDT (c = 1 cal/g/ºC for water)
• Heat of fusion: Q = mL_f (L_f = 80 cal/g for water)
• Heat of vaporization: Q = mL_v (L_v = 540 cal/g for water)
• Heat transport: conduction, convection, radiation
• First law of thermodynamics: Q = DU + W
• Work done by expanding gas: W = PDV
• Second law of thermodynamics: e = 1 - Q_c/Q_h < 1 - T_c/T_h < 1
• Entropy: DS = DQ/T (always increases for Universe)

Sound

• Hooke's law: F = -kx
• Frequency for mass on spring: w = (k/m)^1/2
• f = w/2p = 1/T (T is the period)
• Frequency for pendulum: w = (g/L)^1/2
• Velocity of wave: v = fl (l is the wavelength)
• Velocity of wave on a string: v = (F/m)^1/2
• Velocity of sound in air: v = 331 m/s [1 + T(ºC)/273]^1/2
• Sound intensity: I = P/A (power per unit area)
• Sound level: dB = 10 log₁₀(I/I₀) (decibels)
• I₀ = 10^-12 W/m² (approximate threshold of hearing)
• Doppler effect: f ' = f(v+ v₀)/(v - v_s)
• Resonance on strings and in air columns
• Beat frequency: f_B = |f₁ - f₂|

Closing Comments

• Basic science / Applied science
• Theory / Experiment
• Objective / Subjective
• Known / Unknown
• What? / Why?
• Hard science / Soft science
• Science / Humanities - Religion