Chapters 8, 10 & 11

Chapters 8, 10 & 11

1. Chapter 8

   • Rotational Motion
     • Angular velocity describes how the angular position is changing with time. ω is the symbol for angular velocity
       • Average angular velocity found by dividing the change in angle over the change in time.
         • Counterclockwise means positive angular velocity
         • Clockwise means a negative angular velocity
       • Instantaneous angular velocity is equal to the average angular velocity when ω is constant
     • Angular acceleration is the rate of the change in the angular velocity over hte change in time
     • One revolution of an object is equal to 2pi radians
       • Period = T = 2*pi / ω
   • Torque
     • Torque is the product of an applied force and the distance it is applied from the support point
     • When the force is perpendicular to the pivot point, T equals force times distance from pivot point
     • Rotational equilibrium is when torque is equal to 0.

2. Chapter 10

   • Pressure
     • Pressure is found by the force divided by the area of the cross section
       • Measured in Pascals (Pa)
         • Atmospheric pressure is equal to 1.01 * 10^5 Pa
         • 1 Pa = 1 N/m^2
     • P = F/A
   • Density
     • Density is defined as mass per unit volume
       • Units of kg/m^3
   • Specific Gravity
     • The ratio of the density of a substance to the density of water
       • If liquid is at equilibrium then the sum of F = 0
         • Sum of y F = P(bot)A - P(top)A - mg = 0
           • P (bot) - P (top) = pgh
     • Fluid Gravity
       • P (atm) = p(density)gh
   • Buoyant Force
     • Fb = (density of liquid)gV
     • Apparent Weight is lower when submerged in water
   • Pascal's Principle
     • FL = FR(AL/AR)
   • Principle of Continuity
     • vLAL = vRAR
     • Flow Rate is Q = vA
   • Bernoulli's Equation
     • P1 + 1/2pv^2 + pgh = P2 + 1/2pv^2 + pgh
       • F total = (Pbot - Ptop) A

3. Chapter 11

   • Harmonic Motion
     • Motion in which an object moves along a repeating path over and over again
     • Oscillatory Motion
       • Period (T) is the time it takes to go through one complete cycle
         • Frequency (f) is the number of oscillations in one unit of time
           • f = 1/T T= 1/f
   • Simple Harmonic Motion
     • The y-component is found by A sin 0 = A sin wt = A sin (2pi f t)
       • The x component is found by A cos 0 = A cos (wt) = A cos (2pi f t)
   • Hooke's Law
     • F (spring) = -kx
       • x is the amount the spring is stretched or compressed away from its relaxed position
         • Block is at equilibrium when x = 0
       • F = -kx = ma
   • Pendulum
     • frequency is f = 1/2pi * square root of g/L
   • Energy
     • 1/2mv(max)^2 = KEmax = PE max = 1/2kA^2
   • Stress and Strain
     • F/A = y(change in L/L)
     • Shear Strain
       • F/A = S(x/L)
     • Bulk Modulus
       • P = B(V/V original)