# 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= V_{o}+ at

Δx = V_{o} t + (1/2) a t^{2}

V^{2} = V_{o}^{2} +2aΔx

Δx = ∫ v(t) dt

Δv= ∫ a(t) dt

V_{avg} = Δx/Δt = (X_{f} - X_{o})/(t_{f} - t_{o})

V= dx/dt

a= dv/dt

UCM/gravitation

F_{c} = mv^{2}/ r

a_{c }= v^{2}/r = w^{2}/r

Fg= GMm/r^{2}

U_{g}= -GMm/r

Rotational Motion

S= Өr

v= wr

a= αr

w= ΔӨ/Δt

a_{c}= w^{2}r

V_{linear} = 2πr/t

parallel axis theorem: I = I_{o} +md^{2}

KE_{roll}= (1/2)I_{cm}w^{2} + (1/2)mv^{2}

Angular momentum (L) = r x p = mvrsinӨ = mwr^{2}sinӨ

dL/dt = Torque

L= w I

K= (1/2) I w^{2}

Moment of Inertia

I = Σm_{i}(r_{i})^{2} = ∫r^{2}dm

I_{solid disk} = (1/2) mR^{2 }(also works for a cylinder about its axis)

I_{hoop }= mR^{2}

I_{solid sphere} = (2/5)mR^{2}

I_{hollow sphere} = (2/3)mR^{2}

I_{rod about center} = (1/12)mR^{2}

I_{rod about end} = (1/3)ml^{2}

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

r_{cm} = Σmr/Σm = ∫r dm / Σm

X_{cm }= (m_{1}x_{1} + m_{2}x_{2})/ (m_{1}+m_{2})

Drag force

Fd = bv = cv^{2}

V_{T} = mg/b

V = V_{T}(1 - e^{(-b/m)t})= (mg/b)(1 - e^{(-b/m)t})

Friction

F_{f}= μ F_{n}

...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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