Find out moment of inertia of circular area, Mechanical Engineering

Find out Moment of Inertia of circular area:

Find out Moment of Inertia of circular area of radius a = 10 cm about its centroidal axis OX as illustrated in Figure

1262_Find out Moment of Inertia of circular area.jpg


 Let a thin strip of width By at distance y from axis OX where,

y = a sin θ    and      By  = 2 (a cos θ)

∴ dy = a cos θ d θ

dA =  By  dy = (2 a cos θ) a cos θ d θ

1760_Find out Moment of Inertia of circular area1.png

All elements ought to be considered for values of θ ranging from - 90o to + 90o + 90o

1468_Find out Moment of Inertia of circular area2.png

Now that

cos 2 θ = cos2 θ - sin 2 θ = 2 cos2 θ - 1

∴ 2 cos2 θ = 1 + cos 2 θ


cos 4 θ = 1 - 2 (sin 2 θ)2

∴ 2 (sin 2 θ)2  = 1 - cos 4 θ

∴ Ix   =  a4/2 ∫  2 [ sin 2 θ]2  d θ =  a4/2 ∫ (1 - cos 4 θ) d θ


= π a 4 / 4

= π D 4/64 ,  where D = diameter of circle = 2 a

∴ I x = π× 10 4 /4 = 7854 cm4 .

This is to be noted down that circular cross-section is axis-symmetric, that means it is symmetric w.r.t. both x and y axes or any other radial direction and also has similar nature of shape regarding all centroidal axes.

1046_Find out Moment of Inertia of circular area3.png

∴ Iy   = Ix   =  πa4  /4= π a2   (a2/4) =   A (a2/4)        

where, A = Area of the circle of radius a.

Letting perpendicular axis theorem, we have following :

I z  = I x  +  I y  =  A (a2/2)

Posted Date: 1/29/2013 1:26:41 AM | Location : United States

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

Write discussion on Find out moment of inertia of circular area
Your posts are moderated
Related Questions
Question: Characterisation tests have been performed on a four pole, 415 V (line to line), three phase, star connected, 50Hz induction motor, with the following results:

Ask question #Minimum 1. Research the topic of heat loss in a cylindrical pipe. Explain which laws of physics are used to discuss heat loss in a pipe, and briefly explain how the f

Illustrate in brief the types of power plant? Illustrate the factor to be considered for site selection in hydro power plant? a) Compare stream power plant with hydro power p

Pneumatic system is a system that uses air to power something. For example, have you seen the tube systems at bank drive-up tellers? Air is used to drive the tubes back and forth f

What is Spot welding equipment? Spot welding machines may by classified as follows on the basis of mechanical Construction; 1. Rocker-arm Machines 2. Press-type machin


Q. What is the use of welding electrode? An electrode is a piece of wire or a rod (of a metal or alloy), with or without flux covering, which carries current for welding. Its o

a) Describe and illustrate the terms with their classification: Mechanism, Kinematic, Machine links and Kinematic pair. b) Discuss the Inversions of double slider crank chain an

Q. Steam and Power Generation Equipment? Locating steam and power generation equipment outside of the process areas ensures that critical facilities feeding major portions of t

Determine the width and depth of the beam: A timber beam of rectangular section is only supported over a span of 5 m. It carries an uniformly distributed load of 15 kN/m over