Physics MidTerm 1 Cheat Sheet

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

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

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-final`² = (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)

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)

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)

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

Physics MidTerm 1 Cheat Sheet by brandenz1229