Reference Guide

Equation Reference 5-47
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
3
---
r
2
h⋅ ⋅=
A π r
2
⋅ π r r
2
h
2
+⋅ ⋅+=
Ixx
3
20
------
m r
2
⋅ ⋅
3
80
------
m h
2
⋅ ⋅+=
Izz
3
10
------
m r
2
⋅ ⋅=
Id Ixx m d
2
⋅+=
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_kg ∗ m^2, Izz=0.0180_ kg ∗ m^2,
Id=0.0312_ kg ∗ m^2.