Physics Equations: Mechanics
Having trouble on the 4 minute drill? Need to consolidate your thoughts for the Mechanics part of the AP-C exam? Have no fear! I've sifted through my notes to find a good portion of the mechanics equations. If you find anything missing/incorrect, PLEASE give feedback in the comments section! I'll edit the changes in ASAP. Thank you
MECHANICS
Vectors etc.
A B = lAl lBl cos Ө
A x B = - (B x A)
lA x Bl = lAl lBl sin Ө
Kinematics
V= Vo+ at
Δx = Vo t + (1/2) a t2
V2 = Vo2 +2aΔx
Δx = ∫ v(t) dt
Δv= ∫ a(t) dt
Vavg = Δx/Δt = (Xf - Xo)/(tf - to)
V= dx/dt
a= dv/dt
UCM/gravitation
Fc = mv2/ r
ac = v2/r = w2/r
Fg= GMm/r2
Ug= -GMm/r
Rotational Motion
S= Өr
v= wr
a= αr
w= ΔӨ/Δt
ac= w2r
Vlinear = 2πr/t
parallel axis theorem: I = Io +md2
KEroll= (1/2)Icmw2 + (1/2)mv2
Angular momentum (L) = r x p = mvrsinӨ = mwr2sinӨ
dL/dt = Torque
L= w I
K= (1/2) I w2
Moment of Inertia
I = Σmi(ri)2 = ∫r2dm
Isolid disk = (1/2) mR2 (also works for a cylinder about its axis)
Ihoop = mR2
Isolid sphere = (2/5)mR2
Ihollow sphere = (2/3)mR2
Irod about center = (1/12)mR2
Irod about end = (1/3)ml2
Torque (T)
x >> Ө
v >> w
a >> α
m >> I
F >> T
ΣF = ma >> ΣT = Iα
T = rxF = rFsinӨ
T = (Radius)(tension)
Center of Mass
rcm = Σmr/Σm = ∫r dm / Σm
Xcm = (m1x1 + m2x2)/ (m1+m2)
Drag force
Fd = bv = cv2
VT = mg/b
V = VT(1 - e(-b/m)t)= (mg/b)(1 - e(-b/m)t)
Friction
Ff= μ Fn
...As to not get long and confusing, I'll make another blog post with all of the Electricity & Magnetism equations that I have in it. Check that post out, too!
--Alpha Geek
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