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Physics MidTerm 1 Cheat Sheet by

Chapter 1 - 5 Formulas

Chapter 1 Unit(s) / Mechanics / Sig-Figs / Vectors

Speed = (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 Formula

x = (-b +/- √b2 - 4 ⋅ a ⋅ c ) / (2 ⋅ a)
 

Chapter 2: Motion along A Straight Line

One 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 Motion

The 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 Laws

Superp­osition 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 Laws

vector-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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