1. Dot Product A · B
    A · B = [A][B]cosθ

    You get a scalar product.
  2. Cross Product A x B
    A x B = [A][B]sinθ

    You get a vector product.
  3. Displacement vs Distance
    • Displacement: includes the magnitude and direction of only the net change from start to finish
    • Distance: a scalar quantity that takes into account to length traveled
  4. Velocity vs Speed
    • Velocity: magnitude of measured rate of change of displacement per unit of time (vector quantity)
    • Speed: rate of actual distance traveled divided by a given unit of time
  5. Instantaneous Velocity
    v = lim(as Δt → 0) Δx/Δt
  6. Unit of Force
  7. Net Force
    Newton's second law of thermodynamics

    • F = ma
    • m: mass
    • a: acceleration
  8. Gravity
    Fg = (Gm1m2)/(r2)

    • G: 6.67x10-11 N·m2/kg2
    • r: distance between the two object of m1 and m2
  9. Static Friction
    Exists between two objects at rest. It is an equal and opposite force acting on object.

    0 ≤ fs ≤ μsN

    • μs: coefficient if static friction
    • N: normal force (component of force perpendicular to the plan between object on at rest and surface)
  10. Kinetic Friction
    Exists between two objects sliding along a surface. 

    fk = μfN

    • μf: coefficient if kinetc friction
    • N: normal force (component of force perpendicular to the plan between object on at rest and surface)
  11. Relate coefficient of static friction to kinetic friction
    μs > μk
  12. Weight
    A measure of gravitational on an objects mass.

    Fg = mg

    g: 9.8 m/s2
  13. Center of Mass
    Image Upload 1
  14. Average Acceleration
    A = Δv / Δt
  15. Linear Motion Equation
    (no x value)
    v = v0 + at
  16. Linear Motion Equation
    (no v value)
    x = v0t + at2/2
  17. 'Linear Motion Equation
    (no t value)
    v2 = v02 + 2ax
  18. Linear Motion Equation
    (no v0 or a value)
    x = vt
  19. Two gravity equation for an inclined plane
    • Fg,ll = mgsinθ = ma
    • Fg,(perpendicular) = mgcosθ = N
  20. Centripetal Force
    Fc = mv2/r

    (centripetal acceleration)

    • Note:
    • Centrifugal force is antiparrallel to centripetal force
  21. Translational equilibrium
    Exists only when the vector sum of all forces is 0
  22. Fulcrum
    Fixed pivot point
  23. Torque
    Application of force at some distance from the fulcrum.

    τ = r x F = (r)(F)sinθ

    r: distance of applied force from fulcrum
  24. τ sign when rotated clockwise / counterclockwise
    • Counterclockwise (-)
    • Clockwise (+)
  25. Normal force exerted by fulcrum
    • n = Fg,seesaw + blocks
    • N = (mseesaw + m1 + m2)g
  26. Equation for kinetic energy
    Kinetic Energy: energy of motion

    K = (1/2)mv2
  27. How is kinetic energy related to speed and velocity?
    It is NOT related to velocity, but it IS related to speed.

    The faster something is, the more kinetic energy it has, hense K = (1/2)mv2
  28. Potential Energy Equation
    Potential Energy: energy with the potential to do work of stationary objects

    U = (1/2)mgh
  29. Elastic Potential Energy
    When a spring is stretched from it's equilibrium length, the spring has spring potential energy determined by the following equation:

    U = (1/2)kx2

    • k: spring constant (high k means spring is stiffer)
    • x: magnitude of displacement from the equilibrium length
  30. Total Mechanical Energy
    The sum of the objects potential and kinetic energy.

    E = U + K

    This is if the system is conserved (no energy leaves system due to things like friction, heat, light)
  31. Two commonly encountered conservative forces
    • Conservative Forces: those that are path independent and do not dissipate energy
    • -gravitational
    • -electrostatic

    If the net change is 0, then the forces are conserved.
  32. Nonconservative Forces
    • Forces that dissipate mechanical energy as thermal or chemical energy:
    • -friction
    • -air resistance
  33. Equation for conservation of energy when work done by nonconservative forces is 0
    ΔE = ΔU + ΔK = 0 = W

    (work is measured in J)
  34. Work done by nonconservative forces
    Wnonconservative = ΔE = ΔU + ΔK

    (work is measured in J)
  35. Work Equation when something exerts forces on something else
    Work: it is not a form of energy, but the process by which energy is transferred from one system to another

    W = F · d = Fdcosθ

    θ: the angle between force vector and displacement vector

    (work is measured in J)
  36. Isovolumetric or Isochoric process
    In a P vs V diagram, this is when no work is done. This means volume does not change, ONLY pressure.
  37. Calculating work in a Isobaric process
    Isobaric: when pressure is constant, and only volume changes.

    W = PΔV

    The area under a P vs. V line is work.

    (work is measured in J)
  38. How would you calculate work when P and volume is not constant?
    It would be the area under the curve. Try cutting it up into shapes who's areas you know and calculating the area.

    (work is measured in J)
  39. What does it mean to have (+) work? (-) work?
    • (+): work is done by a system
    • (-): work is done on a system

    (work is measured in J)
  40. Power Equation
    Power: rate at which energy is transferred from one system to another.

    P = W/t = ΔE/t

    (work is measured in J)
  41. Work-Energy Theorum
    Mechanical application for relating energy and work. The net work done by forces acting on an object result in equal change in the objects kinetic energy:

    • Wnet = ΔK = Kf - Ki
    • Knowing the magnitude of forces acting on an object allows you to calculate the work.

    (work is measured in J)
  42. Mechanical Advantage
    Mechanical Advantage: ratio of magnitudes of the force exerted on an object by a simple machine (Fout) to the force applied on a simple machine (Fin).

    Mechanical Advantage = Fout/Fin
  43. Calculating Efficiency of a Pulley
    Efficiency = Wout/Win = [(load)(load distance)]/[(effort)(effort distance)]

    • load: weight (mass x gravity)
    • load distance: object height lifted
    • effort: force required to lift crate
    • effort distance: how much rope must be pulled (height raised x number of pulleys)

    You don't always get 100% efficiency because of nonconservative forces.
  44. What are the six simple machines?
    • Inclined plane
    • Wedge
    • Pulley
    • Liver
    • Wheel and axle
    • Screw
  45. How can you calculate the force being used to pull a weight on a pulley, given a mass and acceleration?
    The force used to pull up the pulley is F = ma. The tensions on the pulley cancel force done by gravity if it was still but increase as tension increases, giving:

    Fnet = ma = xT - mg

    x: number of ropes used
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