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Physics Equations: Mechanics


AlphaGeek

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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 36f8ae4c86b69d52d037a6802d91cc4a.png 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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