Solid Geometry (12)

Variable

Description

 

 

A

Total surface area

b

Base length

d

Distance to rotation axis in z direction

h

Height in z direction (Cone, Cylinder), or

Height in y direction (Parallelepiped)

 

I, Ixx

Moment of inertia about x axis

Id

Moment of inertia in x direction at d

Izz

Moment of inertia about z axis

m

Mass

r

Radius

t

Thickness in z direction

V

Volume

 

 

Reference: 4.

 

Cone (12, 1)

Equations:

V =

π

2

⋅ h

A = π ⋅ r

2

+ π ⋅ r ⋅

r

2

+ h

2

-- ⋅ r

 

 

 

 

 

3

 

 

 

 

 

 

 

 

 

3 ⋅ ⋅ 2 3 ⋅ ⋅ 2 Ixx = ----- m r + ----- m h

20 80

Id = Ixx + m ⋅ d2

Izz =

3

⋅ m ⋅ r

2

-----

 

 

10

 

 

Example:

Given: r=7_cm, h=12.5_cm, m=12.25_kg, d=3.5_cm.

Solution: V=641.4085_cm^3, A=468.9953_cm^2, Izz=0.0162_kgm^2, Izz=0.0180_ kgm^2, Id=0.0312_ kgm^2.

Equation Reference 5-47