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Chapter 1 Unit(s) / Mechanics / Sig-Figs / VectorsSpeed = (d/t) || (m/s) | d = distance : m = meters | | | t = time : s = seconds | 1 km = 1000 m | 1 kg = 1000 g | mass = (kg) | 1 hour = 3600 seconds | time = (seconds) | 1 mile = 1.609 km | length = (meter) | Volume = 1 cm3 | Sig Figs | π = 3.14 (3 sigfig) | π = 3.14159 (6 sigfig) | Density = (mass / volume) || (kg / m3) || (g / cm3) | √ = square root | Vector (Displacement) = √(x)2+(y)2 | Total distance = x + y | Vector A = Vector B if |Vector A| = |Vector B| | Magnitude: √(x)2+(y)2 = (Answer in Units) : 1 Direction | Components of Vector | Vector A = Ax + Ay | Ax = A ⋅ cos(Θ)
Ay = A ⋅ sin(Θ) | A = √(A ⋅ cos(Θ))2 + (A ⋅ sin(Θ))2 | Θ = Angle | x = cos(Θ)
y = sin(Θ) | cos(Θ) = Ax / A
sin(Θ) = Ay / A | tan(Θ) = (y / x) or (Ay / Ax) or (By / Bx) | x = Î
y = ĵ
z = k̂ | Vector A = AxÎ + Ayĵ
Vector B = BxÎ + Byĵ | Vector R = Vector A + Vector B
Vector R = (Ax + Bx)Î + (Ay + By)ĵ
Vector R (direction) = (x)Î + (y)ĵ
Vector R (magnitude) = √(x)Î2 + (y)ĵ2 |
Quadratic Formulax = (-b +/- √b2 - 4 ⋅ a ⋅ c ) / (2 ⋅ a) |
| | Chapter 2: Motion along A Straight LineOne Dimensional Motion | Average Speed = (total distance) / (time)
| Displacement = Final Point - Initial Point
| Not Constant Velocity | Average Velocity (V) = (displacement / time)
| Average Velocity (V) = (∆x / ∆t)
| Instantaneous Velocity = derivative of the given equation
Instantaneous Velocity = ( (a-final) - (a-initial) ) / ( (t-final)-(t-initial) ) | ∆t = (t-final) - (t-initial) | ∆x = (x-final) - (x-initial) | Acceleration | ∆V = (V-final) - (V-initial)
∆t = (t-final) - (t-initial) | Acceleration (a) = (∆V) / (∆t)
[a is constant] | if a > 0 (positive)
if a < 0 (negative) | Instantaneous Acceleration = derivative of the given equation | Constant Acceleration
= constant acceleration motion in 1D | V-final = (a ⋅ t) + V-initial
V-final2 = (v-initial)2 + 2 ⋅ a ( (t-final) - (t-initial) )
| ∆x = (x-final) - (x-initial)
∆x = (v-average) ⋅ (seconds)
∆x = (1/2 ⋅ (V-final) + (V-initial) ) ⋅ t (seconds) | x-final = 1/2 ( (V-initial) + (V-final) ) ⋅ t + (x-initial)
x-final = x-initial + (V-initial) ⋅ t(seconds) + 1/2 ⋅ a ⋅ t2
| Gravity (g) = -9.8 m/s2 | V-final = (V-initial) + g * t (seconds) |
| | Chapter 3: 2D or 3D MotionThe Acceleration Vector | a = ∆V / ∆t | (v-final) = (v-initial) + ∆V
∆V = (v-final) - (v-initial)
∆V = (v-final) + (-(v-initial)) | Constant Speed Changing Direction | a = ∆V / ∆t | (v-final) = (v-initial) + ∆V
∆V = (v-final) - (v-initial) | Projectile Motion
two assumptions: | 1. The freefall acceleration (g) is constant
2. Air resistance is negligible | y-direction = constant acceleration motion
x-direction = constant velocity motion
Acceleration is only negative (y-direction)
g = -9.8 m/s2 | Constant Velocity Motion | x = (x-initial) + (v [x-direction] ) ⋅ t | V (y-direction) = (v-initial) [y-direction] + g ⋅ t | (y-final) = (y-initial + (v-initial) [y-direction] ⋅ t + 1/2 ⋅ g ⋅ t2 | V (y-direction)2 = (v-initial) [y-direction]2 + 2 ⋅ g ( (y-final) - (y-initial) ) | V (y-direction) = (v-initial) [y-direction] + g ⋅ t | Trig Identity | sin(ΘΘ) = sinΘcosΘ + cosΘsinΘ | Constant Speed Motion
velocity is always changing | r = radius | V = (2πr)2 : 4π2r | T = time-period | a = ∆V / ∆t : never zero
∆V = (V / r) · ∆r | Centripetal Acceleration | Ac = (V2) / r
Ac = (2πr)2 / r
Ac = 4π2r / T2 | Tangential and Radial Acceleration | Ac = a-rad | Vector A-total = Vector A-tangential + Vector A-radical
A-total = √(A-tan)2 + (A-rad)2 | Relative Motion | r ' = ( (v-initial) ⋅ t ) - (vector-r) | Vector-r = √( (v-initial) ⋅ t)2 + (r ')2 | Vector-V ' = (v-final) - (v-initial) |
| | Chapter 4: Newtons LawsSuperposition of Forces | Vector-R = Vector-F1 + Vector-F2 | N = Net Force | Fx = N · cos(ϴ)
Fy = N · sin(ϴ) | Rx = ∑Fx
Ry = ∑Fy | R = √(Rx)2 + Ry2 | Newton's 1st Law
No Force; No Acceleration; No Motion | Inertia:
the tendency of an object to resist any attempt to change its velocity | Newton's 2nd Law | Net Force = m · g | a (x-direction) = (Fx total) / mass
a (y-direction) = (Fy total) / mass | tan(ϴ) = y / x | Newton's 3rd Law | Fn = Normal Force | Fy = Fn - m · g · cos(ϴ) | Fx = m · g · sin(ϴ) |
Chapter 5: Applying Newton's Lawsvector-F = m · a | Fx = m · ax | T = tension : friction | Fy= m · ay | y = T - m · g | Fr = Fn : Normal Force (Fn) | No Friction | α = Coefficient | Fn = m · g | Fx = T1· cos(ϴ) + T2· cos(ϴ) | | | Fy = T1· sin(ϴ) + T2· sin(ϴ) | Friction | Static Friction (fs): Object not in motion
Kinetic Friction (fK): Object is in motion | | | Empirical Formula | μk: Coefficient of Kinetic Friction
μs: Coefficient of Static Friction
Static: fs ≤ μs · Fn
Static: fk = μk · Fn | | | Terminal Speed | Fr α v | | | Fr α v2 | Uniform Circular Motion | Fc = m · ac : m · V2 / r | Vertical Circle | Top: Fy = -m · (V2 / r)
Bottom: Fy = μs * m · (g + V2 / r)
maxV = √(fs · r) / m
maxV = √ μs · g · r | Top View | T · sin(ϴ) = m · ac
ac = tan(ϴ) · g |
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