Compute the centroidal moment of inertia, Mechanical Engineering

Compute the centroidal moment of inertia:

Compute the centroidal moment of inertia of a thin homogeneous bar AB of length l and having a mass of m kg

Solution

The mass centre of the bar is at mid point. Further, it is supposed that the zo axis coincides with the axis of the bar. The whole mass of the bar is m.

The elementary mass of the body of length dz may be written as

dm = (m/ l) dz

The coordinates of the point where this elementary mass is situated is (0, 0, zo).

Thus, from Eq. we have

                          =(1/12)ml2

I zo = I xo yo = I yo zo = I zo xo   = 0

The moment of inertia around the axis x passing through the end A may be calculated by substituting zc  = (½) l , in the parallel axis theorem.

Then from Eq. we have

Ix  = Iy  = ml2/12   + m ((1/2) l )2 = (1/3) ml 2

Posted Date: 1/29/2013 6:25:48 AM | Location : United States







Related Discussions:- Compute the centroidal moment of inertia, Assignment Help, Ask Question on Compute the centroidal moment of inertia, Get Answer, Expert's Help, Compute the centroidal moment of inertia Discussions

Write discussion on Compute the centroidal moment of inertia
Your posts are moderated
Related Questions
Compute the utilization of peak capacity: If the fabrication department of the engine manufacturer, operated under ideal conditions, produces 100 engines per day. Management b

Friction: you have learnt laws of friction and problems involving dry friction. The relative sliding motion of one body on another body is resisted by forces called as frictio

CO2 Welding CO2 Welding is a variation of GMAW. Here the inert gas is replaced by gas mixtures or carbon dioxide, which are chemically active. The carbon dioxide decomposes in

Q. Erosion-Corrosion In Sand Slurry Line? All sands are collected in the Inlet Slug Catcher and routed to the Desand Tank for separation. Sand Slurry lines are subject to erosi

send me pipe designing material

Resultant of Non-coplanar Force System: The resultant of a system of coplanar forces can be attained by adding up two forces through law of parallelogram at a time and after t

Roller conveyors are flat circular or spiral. They consist of rollers supported in frames over which materials are allowed to move. They are driven through gravity. Genera


Problem A cat walks along a uniform plank that is 5.00 m long and has a mass of 9.00 kg.  The plank is supported by two sawhorses, one 0.500 m from the left end of the board a