Physics Final Cheat Sheet Cheat Sheet by brandenz1229

s = speed	t = time
Total Distance	xf+xi
One Dimens­ional Motion
Distance	d = s⋅t
Displa­cement	xf-xi
Speed	(xf+xi) / (tf+ti`)
Not Constant Velocity
Average Velocity	(xf-xi) / (tf-ti`)
x↑: v+ x↓: v- x→: v=0	a+: v↑ a-: v↓ a=0: v→
Instan­taneous Accele­ration
(vf-vi) / (tf-ti`)
Constant Accele­ration in 1D
Vf = Vi + (a⋅t)
Constant Accele­ration Final Distance
Xf= 1/2(Vf-Vi) ⋅ t
Xf= Xi + (Vi⋅ t) + 1/2(a ⋅ t)
a = (Vf-Vi) / t	t = (Vf-Vi) / a
Vf = Vi⋅ a2
Vf2 = Vi2 + 2⋅a (xf-xi)
Gy = -9.8 m/s

Angular Frequency	w = 2πf 2π/T
Frequency	f = 1 / T
Period	T = 1 / f
Restoring Force	Fx = -kx
Simple Harmonic Motion
k = Spring Constant	x = displa­cement
m = mass
Displa­cement as function of time	x = Acos(wt + Θ)
Velocity as function of time	v = -wAsin(wt + Θ)
Accele­ration as function of time	a = -w2Acos(wt + Θ)
xmax = A [Ampli­tude]	-xmax = A [Ampli­tude]
vmax = wA	-vmax = wA
amax = w2A	-amax = w2A
Equation for Simple Harmonic Motion	a`x = - (k/m) x
k = restoring force
Angular Frequency for SHM	w = √k/m
Frequency for SHM	f = w/2π
	f = 1/2π√k/m
Period for SHM	T = 1/f
	T = 2π/w
	T = 2π√m/k
Total Mechanical Energy (Constant)	E = 1/2mvx2 + 1/2kx2
	E = 1/2kA2

1km = 1000m	1 kg = 1000g
Dot Product	P = Power
A⋅B = (Ai⋅Bi)+(Aj⋅Bj)	t = s
Work = Force ⋅ distance
W = Fx⋅ distance
W = F⋅cosΘ­⋅di­stance
KE: 1/2⋅m⋅v2	U = m⋅g⋅h
Wtotal = KEf - KEi
Wx = F (cosΘ)⋅s || Wy = F (sinΘ)⋅s
Constant Speed
Friction (opposite) = cos(180o)
P = F⋅v	P = (W/t)
Pav= ΔW / Δt [Average Power]	if F→ & s← = - W
if F↓ & s→ = 0	if F→ & s→ = W
Force Required to Stretch a spring
Fx = k ⋅ x

GE= 6.67⋅10-11	Earth Gravity Constant
RE= 6.38⋅106 m	Earth Radius
ME= 5.972⋅1024 kg	Mass of Earth
g = 9.8 m/s; ag = 9.8 m/s	r - RE = h
Fg = (GE⋅m1⋅m2) / (r2)	Fg = m ⋅ a
w = m⋅g	s = r - RE cosΘ
Gravit­ation and Spheri­cally Symmetric Bodies	Fg = (GE⋅mE⋅m) / (r2)
Weight of the body at Earth's Surface	w = Fg = (GE⋅mE⋅m) / (RE2)
Accele­ration due to Gravity	g = (GE⋅mE) / (RE2)
Velocity of Earth	VE= 4/3πRE2 = 1.08⋅1021 m3
Gravit­ational Potential Energy
U = -(GE⋅mE⋅m) / (r)
WorkDone by Gravity	Wgrav = m⋅g(r1-r2)
Wgrav = GmE⋅m ⋅ (r1-r2) / (r1⋅r2)
Wgrav= GmE⋅m ⋅ (r1-r2) / (RE2)	[if the body stays close to Earth]
Speed of the Satellite	v = √(G⋅mE / r)
Period of Circular Orbit	T = (2πr / v)
T = 2πr3/2/√G⋅mE	T = 2πr √(r / G⋅mE)
Point Mass Outside a Spherical Shell	Ui= - Gm⋅mi / s
Apparent weight ; Earth's Rotation
w0 = true weight of object	F = force exerted by spring scale
F + w0 = net force on object	w = apparent weight = opposite of F
centri­petal accele­ration`	w0- F = (mv2 / RE)
	w = w0 - (mv2 / RE)
freefall accele­ration	g = g0 - (v2/ RE)
Black Holes
P = Density	P = M / v
v = 4/3πR3	c = speed of light in the vaccum
Schwar­dzs­child Radius	Rs = 2GM / c2
c = √2GM / RS

Y-axis E = Mechanical Energy

Wgrav = F ⋅ s = w(y1-y2)

Wgrav=(m⋅g⋅y1)-(m⋅g⋅y1)

Wgrav=Ugrav,1 - Ugrav,2

Wgrav = -Δ Ugrav

Conser­vation of Mechanical Energy

Kf-Ki = Ugrav,1 - Ugrav,2

Ki+Ugrav,1=Kf+Ugrav,2

E = K + Ugrav = constant (if gravity does work)

When other forces than Gravity do work

Wother + Wgrav = Kf - Ki

Elastic Potential Energy

Uel = 1/2kx2

Work Done a Spring

W = 1/2kx22 - 1/2kx12

If Elastic does work, total mechanical energy is stored

Ki+Uel,1=Kf+Uel,2

Situations with Both Gravit­ational and Elastic Potential Energy

K1+U1+Wother=K2+U2

The work done by all forces other than the gravit­ational force or elastic force equals the change in total mechanical energy E = K + U of the system

The Law of Conser­vation of Energy

ΔUint = -Wother ΔUint = internal energy

Force and Potential Energy

Fx(x) = - dU(x) / dx

The Simple Pendelum (TSP)	L = pendulum length
Angular Frequency TSP	w = √k/m
	w = √mg / L /m
	w = √g/L
Frequency TSP	f = w/2π
	f = 1/2π √g/L
Period TSP	T = 2π/w
	T = 1/f
	T = 2π√L/g
The Physical Pendulum (TPP)
L = angular momentum	L = mvr
w = Angular Velocity	w = ΔΘ / Δt
(I)nertia = L / w
Angular Frequency TPP	w = √mgd / I
Period TPP	T = 2π √ I / mgd
Damped Oscill­ation
b = Damping Constant
Displace of Damped	x = Ae-b(2m)t cost (wt + Θ)
Angular Frequency of Damped	w' = √ (k/m) - (b2 / 4m2)
Force Oscill­ations and Resonance
Fmax = Maximum Driving Force	k = constant restoring force
wd = Driving Angular Frequency
A = Fmax / √(k-mwd2)2 + b2wd2