How Do You Calculate the Moment of Inertia for a Tapered Tube?

[Sud89]

Homework Statement

To calculate the moment of inertia of a cantilevered tapered tube with mid-thickness large radius RL and mid-thickness small radius RS

Homework Equations

The Attempt at a Solution

Area of the larger end of the tube
AL=2*pi*RL*t
Area of the smaller end of the tube
AS=2*pi*RS*t
Area of the tube at a distance x is
AX=2*pi*RX*t
RX=RL - x*tanalpha
tanalpha=deltaR/L
deltaR = RL-RS[/B]

 

[SteamKing]

When you say 'calculate the moment of inertia', do you mean calculate the 'second moment of area' of the cross section of the tube (units of L⁴ ) or do you mean calculate the 'mass moment of inertia' of this piece (units of ML² )? It makes a difference ...

 

[Sud89]

When you say 'calculate the moment of inertia', do you mean calculate the 'second moment of area' of the cross section of the tube (units of L⁴ ) or do you mean calculate the 'mass moment of inertia' of this piece (units of ML² )? It makes a difference ...

Second moment of area

 

[SteamKing]

Second moment of area

How would you calculate the second moment of area for a circle?