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
Define O.R. and what are the applications in Industry ? A firm uses lathe, milling and Grinding machine to make two machine parts. The table below show the machining time requir

Rankine cycle - Thermodynamics: The major problems of Carnot cycle is compressing very wet steam mixture from the condenser pressure up to boiler pressure. The trouble can be

Uniformly Distributed Load and Uniformly Varying Load: Uniforml y Distributed Load (UDL) A UDL is one which is spread over beam in such a manner that the rate of loading

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

Find the minimum weight to keep equilibrium: A belt supports the two weights W 1 an d W 2 over a pulley as shown in the figure given below. If W 1 = 1000N, fi

A Spring - mass system which is subjected to a harmonic force FCoswt. calculate the response of the system, refer figure Given x (0) = 0.01 m x(0) = 0.04 m/sec w = 30 rad/

The steam that leaves the super-heater is expanded from 130bar at 535°C to 25.2bar at 310°C in a high pressure turbine. The steam from the exit of the HP turbine is reheated to 535

how to draw parabola by parallelogram method..?

(a) Write short note on steady flow energy equation and its applications. (b) A heat engine operating between two reservoirs at 1000k and 300k is used to drive a heat pump which