Find out the moment of inertia of an annular area, Mechanical Engineering

Find out the moment of inertia of an annular area:

Find out the M. I. of an annular area among two circles where difference of radius is quite small, around any centroidal axis.

Solution

The centroid G of such a thin circular strip of small thickness t is at its geometrical centre as illustrated in Figure

Figure 4.36

We have, dA = ds × t

where  ds = Arc length = a × d θ

Letting the plane of the area in XOY plane (O and G coincide),

430_Find out the moment of inertia of an annular area.png

= 2 π a3 × t

= 2 π at × a 2

= (Area of annular strip) × a 2

=  A′ a 2

As the annular strip of area A′ is also axis symmetric, then I x  = I y ,

Hence, we have I x  =  I y  =    I z   /2 = A′ a2/2

Posted Date: 1/29/2013 1:28:12 AM | Location : United States







Related Discussions:- Find out the moment of inertia of an annular area, Assignment Help, Ask Question on Find out the moment of inertia of an annular area, Get Answer, Expert's Help, Find out the moment of inertia of an annular area Discussions

Write discussion on Find out the moment of inertia of an annular area
Your posts are moderated
Related Questions
In Tools and equipment we studied about the various tools and equipment used in service and repair of a motorcycle and for the troubleshooting. Acquainting with these will help you

Determine the Brake power of an Engine which is running at a fixed speed of 300 r.p.m. and carries a rope brake Dynamometer. The Dead weight on the spring balance and engine readin

we can use in proove of energy is a propertyof system we can use (E) instead of (dQ-dW)

Derive a regression forecasting equation: The general manager of a company producing road rollers is convinced that the demand for road rollers is associated to the number of

Primitives of b-rep Scheme The building blocks for b-rep. models are : Vertex It is a unique point (an ordered triplet) in space. Edge An edge is a finite, non-


Find out the moment of inertia of an annular area: Find out the M. I. of an annular area among two circles where difference of radius is quite small, around any centroidal axi

Principles Governing Rural Roads Design Standards: The following principles should govern in design of rural roads : (a) Rural Roads are low volume facility serving an acc

Find the value of force to move a system: Th e system of particles shown in the figure given below is initially at rest. Find the value of force F which should be applied so

Q. What do you mean by turret Nozzle? Turret Nozzle - Turret nozzles are large nozzles that can deliver large quantities of water quickly. They are used on very large fires whe