PHYSICS 6 FORMULA SHEET
(may be used for all exams)
Units
1 m = 100 cm = 1000 mm
1 mL = 1 cm3
1 kg = 1000 g
Krot = ½Iω2
Ugrav = mgh
Uel = ½kd2
Wtot, ext = ΔK + ΔU + ΔEint
Geometry
circumference of circle = 2πr
π ≈ 3.14
Circular motion
arad = v2/r
Trigonometry
cos θ = a/c
sin θ = b/c
tan θ = b/a
360° = 2π rad
b
Universal law of gravitation
G ≈ 6.7×10−11 Nm2/kg2
RE ≈ 6400 km
F = Gm1m2/r2
c
θ
a
Kinematics of translational motion
vav = Δx/Δt
aav = Δv/Δt
vav = (v1 + v2)/2
Δx = v1 Δt + aΔt2/2
v22 = v12 + 2aΔx
Gravitational acceleration at sea level
g ≈ 10 m/s2
Newton’s law for translational motion
Fnet = macm
Model for friction
f k = µk N
f s ≤ µs N
Springs
F = −kΔx
Linear Momentum
p = mv
P=Σp
Fnet, ext Δt = ΔP
Center of mass
M = m1 + m2 + …
xCM = (m1 x1 + m2 x2 + …) / M
vCM = P/M
Work and energy
W = F|| Δx
K = ½mv2
Rotational Inertia
I = Σ mr2
I|| = Icm + MD2
Moments of inertia for common bodies
(axis of symmetry through CM unless specified otherwise)
2
ring: MR
disk: (1/2)MR2
solid sphere: (2/5)MR2
spherical shell: (2/3)MR2
rod (axis thru CM and ⊥ to length): (1/12)ML2
rod (axis through end and ⊥ to length): (1/3)ML2
Kinematics of rotational motion
1 rev = 2π rad
θ = arclength/radius
ωav = Δθ/Δt
αav = Δω/Δt
Δθ = ω1Δt + αΔt2/2
ωav = (ω1 + ω2)/2
ω22 = ω12 + 2αΔθ
Relations between linear and angular variables
vtan = rω, vrad = 0
atan = rα, arad = rω2 = vtan2/r
Torque
τ = rFtan = r F = rFsinθ
⊥
Newton’s law for rotational motion
τ net = Iα
Angular momentum
l = Iω
L=Σl
τnet, ext Δt = ΔL
Rolling without-slipping constraint
vCM = rω
Simple Harmonic Motion
a = −ω2x ⇒ x(t) = Acos(ωt + δ)
T = 2π/ω, f = 1/T
harmonic oscillator: ω = √(k/m)
simple pendulum:
ω = √(g/L)
Normal modes of vibration
λf = v
vstring = √(tension/linear density)
vair = 340 m/s
Liquids
ρ = M/V
ρwater ≈ 1 g/cm3
ρHg ≈ 13.5 g/cm3
p = N/A
p = p0 + ρgh
p0 ≈ 105 Pa
Fb = ρVdispg
steady, incompressible flow: vA = constant
...and inviscid: p + ρv2/2 + ρgz = constant
Temperature and Heat
T = (273.16 K) p/ptr (at constant V)
T [°C] = T [K] + 273.15 K
Q = mcΔT
Q = mL
cwater = 4.2 J/(g K)
cice = 2.1 J/(g K)
Lwater = 334 J/g (freeze ⇔ melt)
2260 J/g (condense ⇔ boil)
Notes: