Physics Equations

Chapter 1- Components of vectors

  • Distance = Speed * Time
  • Pi = C/D
  • Displacement on right angle = a^2 + b^2 = C^2 SQR of C
  • SOHCAHTOA
  • Tan = Sin/Cos

Chapter 2- Motion with constant acceleration

  • Average velocity = X2 – X1 / T2 – T1
  • Velocity = Displacement / Time, Speed = Distance / Time
  • Instantaneous velocity = slope of tangent line to the curve at that point
  • Average acceleration = V2 – V1 / T2 – T1
  • Instantaneous acceleration = slope of tangent line to the curve at that point
  • Constant acceleration, or Ax = Vx – V0x / T- 0, or V = V0x + AxT
  • Vav, x = V0x + Vx / 2
  • Vav,x (velocity for any time T) = ½(V0x + V0x + Ax+T) = V0x + ½ AxT. Also, Vav,x = X2 – X1 / T2 – T1
  • Position as a function of time when constant acc. = Vox + ½ AxT = X-X0 /T, or X = X0 + V0xT + ½ AxT2
  • Velocity as a function of position when constant acc. Vx2 = V0x2 + 2Ax (X-X0)
  • Position, velocity, and time when constant acc. = X-X0 (total displacement) = V0x + Vx / 2 * T (useful when Ax is not known)
  • PROPORTIONAL REASONING=
    • Position X = ½ AxT2
    • XA = ½ AxTA2 = TA2 = (TA)2
    • XB = ½ AxTB2 = TB2 = (TB)2
  • Earth g=9.8 m/s2 on moon g= 1.62 m/s2 near sun g= 274 m/s2

Chapter 3- Motion in a plane

  • Velocity in a plane is the same equation as for chapter 2
    • R = √ X2 + Y2
    • Vav = R2 – R1 / T2 – T1
    • Vav,x = change of X / change of T
    • Vav,y = change of Y / change of T
  • Instantaneous velocity in a plane = slope of tangent line to the curve at that point
  • Instantaneous speed = √VX2 + VY2
  • Direction = tan-1 Vy / Vx
  • Average acceleration in a plane = V2 – V1 / T2 – T1
  • A = √Ax2 + Ay2 and theta = tan-1 Ay / Ax
  • Parallel or perpendicular acceleration
  • Projectile motion (equations on page 77)
  • Uniform circular motion (equations on page 86)
  • Relative velocity in a plane (equations on page 88)

Chapter 4- Newton’s laws of motion

  • Forces
  • A= F (magnitude) / m (mass)
  • M= F/A
  • 1N= (1kg)(1m/s2)
  • M1A1 = M2A2
  • Or, M2/M1 = A1/A2
  • ∑Fx = MAx and ∑Fy = MAy
  • W = M*g
  • M = W/g

Chapter 5- Application of Newton’s Laws

  • F (friction force)k = UkN (normal force)
  • Fs ≤ UsN
  • Fspr = -kx (Hooke’s law)

Chapter 6- Circular motion and Gravitation

  • Arad = v2(speed) / R(radius)
  • V(speed) = 2piR (circumference of the circle)/T2
  • Arad= 4piR/T2
  • Fnet=m*(v2/R) (relation of net force to acceleration)
  • Frad= Mv2/R
  • Mg= M(Vmax)2/R, or Vmax= √gR
  • Fgrav= G*(mmE/r2)
  • Decreases by 1/r2 as we get close to center of earth
  • G= 6.674 * 10-11 N * m2/kg2
  • W(weight based on grav from earth) =Fg = G(mmE/RE2)
    • Because mg=w, so mg = G(mmE/RE2)
    • Rearrange and divide by m to give g=(GmE/RE2)
    • Mass of earth = mE = (gRE2/G), and so ME = 5.98 x 1024 kg
  • Weight of an object decreases inversely with the square of its distance from the earth’s center- r=2RE
  • GmmE/R2 = mv2/R, solving for v = √GmE/R
  • V = 2piR/T
  • T=2piR/v = 2piR√R/GmE = 2piR3/2/√GmE
  • Black hole equation (page 178)

Chapter 7- Work and energy

  •    ½ mv2
  •    W= FII(parallel to displacement)s = (Fcos angle)s
  •      Vf2 = Vi2 + 2AS
    • A = (Vf2 – Vi2) / 2S
    • Ftotal = ma = m * (Vf2-i2)/2S
    • Ftotals = ½ MVf2 – ½ MVi2
    • K = ½ MV2
    • Wtotal = Kf – Ki = Delta K
  •    W = F1 delta X1 + F2 delta X2 + F3 delta X3 etc…
  •      F = KX
  •      W = ½ (X)(KX) = ½ KX2
  •      W = ½ KXf2 – ½ KXi2
  •      Wgrav = Ui – Uf = mgyi – mgyf
  •        MgdeltaS cos B = -mgdeltaY
  • Elastic potential energy (page 207)
  • Conservation of energy (page 208-209)
  • Conservative and non-conservative forces (page 212)
  • Power (page 216)
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