Moment of inertia, Physics

A non-uniform rod AB has a mass M and length 2l.The mass per unit lengthof the rod is mx at a point of the rod distant x from A. find the moment of inertia of this rod about an axis, a)through A,

b) through the mid point of AB.
 
Ans) let a element of length dx at adistance x from the point A of the rod.

mass of this element will be dm = mxdx

so moment of inertia of this element about point A is

  dI = dm * x2

for moment of inertia of whole rod perform intigration

I=  ∫dI = o2Ldm * x2

            =o2Lm * x3 dx

            =4mL4

and we know M =o2Ldm

                      = o2Lmxdx

                      =2mL2

so moment of inerta  I =2ML2

Posted Date: 3/8/2013 8:26:30 AM | Location : United States







Related Discussions:- Moment of inertia, Assignment Help, Ask Question on Moment of inertia, Get Answer, Expert's Help, Moment of inertia Discussions

Write discussion on Moment of inertia
Your posts are moderated
Related Questions
Explain corrosion This corrosion can happen either when a conducting liquid is in contact with a metal or when two dissimilar metals /alloys are is partially immersed in a con

Force: push or pull upon an object resulting from the object's dealings with another object. Whenever there is an interaction among two objects, there is a force upon every of

In a very large closed tank the absolute pressure of teh air above the water is 6.01x 10^5 pa. The water leaves the bottom of the tank through a nozzle that is directed straight up

At what velocity a clock should move so that it seems slow by one minute in a day.

an object of mass 5.0 Kilograms initially travelling at 12.0m/s horizontally enters a region where there is a coefficient of kinetic friction of 0.27. a) use the concepts of wor

Can any heat exist without some source of friction?

#question. third law of motion.

A body of mass m1 , moving with velocity u1 collides head  on with a body of mass m2 moving with a velocity u2 the two bodies stick together after the collision the loss of kinetic

Newtons Laws Skydiving Assume the motion of the skydiver below. As the skydiver falls and he encounters the force of air resistance. An amount of air resistance is dependent up

What do you mean by lateral shift? Derive a mathematical expression for lateral shift produced by a parallel sided glass slab for oblique incidence.