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Physics Equations & Inertia List

This document contains a list of equations and identities related to mechanics and moments of inertia. It includes equations for work, kinetic energy, rotational motion, torque, center of mass, and moments of inertia for various rigid bodies including rods, plates, cylinders, and spheres. It also provides trigonometric identities for sine, cosine, and tangent functions.

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justdellix
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79 views2 pages

Physics Equations & Inertia List

This document contains a list of equations and identities related to mechanics and moments of inertia. It includes equations for work, kinetic energy, rotational motion, torque, center of mass, and moments of inertia for various rigid bodies including rods, plates, cylinders, and spheres. It also provides trigonometric identities for sine, cosine, and tangent functions.

Uploaded by

justdellix
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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LIST OF EQUATIONS

m1 r1 + m2 r2 + ...
A · B = |A||B| cos φ rcm =
m1 + m2 + ...
A · B = Ax Bx + Ay By + Az Bz dθ
W =F·s ω=
dt
1 dω d2 θ
W = ∆K = m(v22 − v12 ) α= = 2
X2 dt dt
W = Fi · si ω = ω0 + αt
i 1
dW θ = θ0 + ω0 t + αt2
P = =F·v 2
dt 2 2
ω = ω0 + 2α(θ − θ0 )
Ugrav = mgy vtan = rω
1
Uel = kx2 atan = rα
2
1 2 1 2 1
Won = kxf − kxi = −Wby Krot = Iω 2
2 2 2 Z
X
Wc = −∆U I= mi ri2 = r2 dm
V
U1 + K1 = U2 + K2 = E i

Wnc = ∆Emech U = M gycm


Wfric = −f ∆s I = I0 + M d2
dU A × B = (Ay Bz − Az By ) î + (Az Bx − Ax Bz ) ĵ
Fx = −
dx + (Ax By − Ay Bx ) k̂
p = mv |A × B| = |A||B| sin φ
J = ∆p = Fave ∆t τ =r×F
dp X
F= τz = Iαz
dt
m1 v1 + m2 v2 + · · · = m1 v1′ + m2 v2′ + · · · 1
K = M vcm 2 1
+ Icm ω 2
vA − vB = −(vA ′ ′
− vB ) 2 2

SOME IDENTITIES
opp adj opp
sin θ = ; cos θ = ; tan θ =
hyp hyp adj
sin(α ± β) = sin α cos β ± cos α sin β
cos(α ± β) = cos α cos β ∓ sin α sin β
sin2 φ + cos2 φ = 1

1
LIST OF MOMENTS OF INERTIA
Assume all rigid bodies have uniform density.
1 2
Slender rod, axis through center I = 12 M L

Slender rod, axis through one end I = 31 M L2


1 2
Rectangular plate, axis through center I = 12 M (a + b2 )
Thin rectangular plate, axis along edge I = 31 M a2
Hollow cylinder I = 21 M (R12 + R22 )
Solid cylinder I = 21 M R2
Thin-walled hollow cylinder I = M R2
Solid sphere I = 52 M R2
Thin-walled hollow sphere I = 23 M R2

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