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Cruz de malta...

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Rueda de Ginebra

Rueda de Ginebra

P

3

2

|BP | = 17.3205 mm |AB| = 35 mm

θ B A

STL → http://www.thingiverse.com/thing:2462254

|AP | = 30 mm θ = 29.652o

Centro de masas M=

r CM =

i

mi

Pi

mi r i i mi

M (V) =

rCM =

V

dm =

rdm dm V

RV

=

V

ρ(r )dV r ρ(r )dV dm V

VR

Centro de masas M=

r CM =

i

M (V) =

mi

Pi

mi r i i mi

rCM =

?

V

dm =

rdm dm V

RV

=

V

ρ(r )dV r ρ(r )dV dm V

VR

Centro de masas M=

r CM =

i

mi

Pi

mi r i i mi

M (V) =

rCM =

V

dm =

rdm dm V

RV

=

V

ρ(r )dV r ρ(r )dV dm V

VR

Momento de inercia

[M L2 ] Ix =

Z

Iy =

Z

Iz =

Z

 2  y + z 2 dm  2  x + z 2 dm  2  x + y 2 dm

Momento de inercia

n

In = [M L2 ] Ix =

Z

Iy =

Z

Iz =

Z

 2  y + z 2 dm  2  x + z 2 dm  2  x + y 2 dm

V

h2 dm =

V

h2 ρ(r)dV

h2 = |r|2 − (r · n)2

Momento de inercia

n

In = [M L2 ] Ix =

Z

Iy =

Z

Iz =

Z

Iij =

Ixy = −

 2  x + z 2 dm

Ixz = −

 2  x + y 2 dm

Iyz = −

V

h2 dm =

V

h2 ρ(r)dV

h2 = |r|2 − (r · n)2

 2  y + z 2 dm

2

V

(r δij − xi xj )dm =

V

2

xydm Z

Z

yzdm



Ixx I =  Ixy Ixz

Ixy Iyy Iyz

 Ixz Iyz  Izz

yzdm

(r δij − xi xj )ρ(r)dV

In = n · In > 0

Momento de inercia

n

In = λn 

II I= 0 0

0 III 0

0 0 IIII

 

Teorema de Steiner

Iij =

V

2

(r δij − xi xj )dm



Ixx I =  Ixy Ixz

  O G + M |d|2 δ − d d Iij = I ij ij i j

I zO = IzG + M |OG|2

Ixy Iyy Iyz



Ixz Iyz  Izz

Momento de inercia Significado +sico de los momentos cruzados

fi = −m0 ω 2 r

FI = −Mω 2 r¯

Momento de inercia

Momento de inercia

?

Rueda conducida Centro de masas

Rueda conductora

|BP | = 17.3205 mm

Eje de rotación

B

Centro de masas

P

Ejes principales

Problema plano

|BP | = 17.3205 mm |AB| = 35 mm |AP | = 30 mm θ = 29.652o

P

V ol2 = 3043, 88 mm3 V ol3 = 5698, 61 mm3

θ A

G2 B

IA = ρ

V

(x2 + z 2 )dV =

= ρ 2.18091 × 106 mm5 = = 382.7 m3 mm2 Centro de masas

IG2 = ρ

V

(x2 + z 2 )dV =

= ρ 302468 mm5 = = 99, 7 m2 mm2

z x

Problema plano

|BP | = 17.3205 mm |AB| = 35 mm |AP | = 30 mm θ = 29.652o

P

V ol2 = 3043, 88 mm3 V ol3 = 5698, 61 mm3

θ

G2

A

B

IA = ρ

V

(x2 + z 2 )dV =

= ρ 2.18091 × 106 mm5 = = 382.7 m3 mm2 Centro de masas

IG2 = ρ

V

(x2 + z 2 )dV =

= ρ 302468 mm5 = = 99, 7 m2 mm2

z x d

G2 B

IB = IG2 + m2 d2...