Chapter 1- Components of vectors

- Distance = Speed * Time
- Pi = C/D
- Displacement on right angle = a^2 + b^2 = C^2 SQR of C
**S**OH**C**AH**T**OA- Tan = Sin/Cos

Chapter 2- Motion with constant acceleration

- Average velocity = X
_{2 }– X_{1 }/ T_{2 }– T_{1} - Velocity = Displacement / Time, Speed = Distance / Time
- Instantaneous velocity = slope of tangent line to the curve at that point
- Average acceleration = V
_{2}– V_{1 }/ T_{2 }– T_{1} - Instantaneous acceleration = slope of tangent line to the curve at that point
- Constant acceleration, or A
_{x }= V_{x }– V_{0x }/ T- 0, or V = V_{0x }+ A_{x}T - V
_{av, x }= V_{0x }+ V_{x }/ 2 - V
_{av,x (velocity for any time T) }= ½(V_{0x }+ V_{0x }+ A_{x+}T) = V_{0x }+ ½ A_{x}T. Also, V_{av,x }= X_{2 }– X_{1 }/ T_{2 }– T_{1} - Position as a function of time when constant acc. = V
_{ox }+ ½ A_{x}T = X-X_{0 }/T, or X = X_{0 }+ V_{0x}T + ½ A_{x}T^{2} - Velocity as a function of position when constant acc. V
_{x}^{2 }= V_{0x}^{2 }+ 2A_{x }(X-X_{0}) - Position, velocity, and time when constant acc. = X-X
_{0 (total displacement) }= V_{0x}+ V_{x }/ 2 * T (useful when A_{x }is not known) - PROPORTIONAL REASONING=
- Position X = ½ A
_{x}T^{2} - X
_{A }= ½ A_{x}T_{A}^{2}= T_{A}^{2 }= (T_{A})^{2} - X
_{B }= ½ A_{x}T_{B}^{2 }= T_{B}^{2 }= (T_{B})^{2}

- Position X = ½ A
- Earth g=9.8 m/s
^{2 }on moon g= 1.62 m/s^{2}near sun g= 274 m/s^{2}

Chapter 3- Motion in a plane

- Velocity in a plane is the same equation as for chapter 2
- R = √ X
^{2}+ Y^{2} - V
_{av}= R_{2 }– R_{1 }/ T_{2 }– T_{1} - V
_{av,x}= change of X / change of T - V
_{av,y }= change of Y / change of T

- R = √ X
- Instantaneous velocity in a plane = slope of tangent line to the curve at that point
- Instantaneous speed = √V
_{X}^{2}+ V_{Y}^{2 } - Direction = tan
^{-1 }V_{y / }V_{x} - Average acceleration in a plane = V
_{2}– V_{1 }/ T_{2 }– T_{1} - A = √A
_{x}^{2 }+ A_{y}^{2 }and theta = tan^{-1}A_{y }/ A_{x} - 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/s
^{2}) - M
_{1}A_{1 }= M_{2}A_{2} - Or, M
_{2}/M_{1 }= A_{1}/A_{2} - ∑F
_{x}= MA_{x }and ∑F_{y}= MA_{y} - W = M*g
- M = W/g

Chapter 5- Application of Newton’s Laws

- F (friction force)
_{k }= U_{k}N (normal force) - F
_{s}≤ U_{s}N - F
_{spr }= -kx (Hooke’s law)

Chapter 6- Circular motion and Gravitation

- A
_{rad }= v^{2}(speed) / R(radius) - V(speed) = 2piR (circumference of the circle)/T
^{2} - A
_{rad}= 4piR/T^{2} - F
_{net}=m*(v^{2}/R) (relation of net force to acceleration) - F
_{rad}= Mv^{2}/R - Mg= M(V
_{max})^{2}/R, or V_{max}= √gR - F
_{grav}= G*(mm_{E}/r^{2)} - Decreases by 1/r
^{2}as we get close to center of earth - G= 6.674 * 10
^{-11}N * m^{2}/kg^{2} - W(weight based on grav from earth) =F
_{g}= G(mm_{E}/R_{E}^{2})- Because mg=w, so mg = G(mm
_{E}/R_{E}^{2}) - Rearrange and divide by m to give g=(Gm
_{E}/R_{E}^{2}) - Mass of earth = m
_{E}= (gR_{E}^{2}/G), and so M_{E }= 5.98 x 10^{24 }kg

- Because mg=w, so mg = G(mm
- Weight of an object decreases inversely with the square of its distance from the earth’s center- r=2R
_{E} - Gmm
_{E}/R^{2}= mv^{2}/R, solving for v = √Gm_{E}/R - V = 2piR/T
- T=2piR/v = 2piR√R/Gm
_{E}= 2piR^{3/2}/√Gm_{E} - Black hole equation (page 178)

Chapter 7- Work and energy

- ½ mv
^{2} - W= F
_{II(parallel to displacement)}s = (Fcos angle)s - V
_{f}^{2 }= V_{i}^{2 }+ 2AS- A = (V
_{f}^{2 }– V_{i}^{2}) / 2S - F
_{total }= ma = m * (V_{f}^{2}-i^{2)}/2S - F
_{total}^{s }= ½ MV_{f}^{2 }– ½ MV_{i}^{2} - K = ½ MV
^{2} - W
_{total}= K_{f }– K_{i }= Delta K

- A = (V
- W = F
_{1 }delta X_{1 }+ F_{2 }delta X_{2 }+ F_{3 }delta X_{3 }etc… - F = KX
- W = ½ (X)(KX) = ½ KX
^{2} - W = ½ KX
_{f}^{2 }– ½ KX_{i}^{2} - W
_{grav}= U_{i}– U_{f}= mgy_{i}– mgy_{f} _{ }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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