Solid Geometry (12)
Variable | Description | |
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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) | ||
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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 | |
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Reference: 4. |
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Cone (12, 1)
Equations:
V = | π | 2 | ⋅ h | A = π ⋅ r | 2 | + π ⋅ r ⋅ | r | 2 | + h | 2 |
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3 ⋅ ⋅ 2 3 ⋅ ⋅ 2 Ixx =
20 80
Id = Ixx + m ⋅ d2
Izz = | 3 | ⋅ m ⋅ r | 2 |
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| 10 |
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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.
Equation Reference