# Final Exam Review Physics 103 - Spring 98

Note: There is no guarantee that everything on the exam is mentioned here, but most things are.

### 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 WNC = 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 Fext = 0
• Elastic versus inelastic collisions

### Rotations

• q = s/r, w = v/r, a = a/r
• Centripetal acceleration: ar = 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 text = 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
• Average molecular kinetic energy: Eav = 3NkT/2
• Heat: Q = mcDT (c = 1 cal/g/ºC for water)
• Heat of fusion: Q = mLf (Lf = 80 cal/g for water)
• Heat of vaporization: Q = mLv (Lv = 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 - Qc/Qh < 1 - Tc/Th < 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 - vs)
• Resonance on strings and in air columns
• Beat frequency: fB = |f1 - f2|