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
Why different colours of white light travell with different speed in a glass prism,while they travell with same speed in air? Ans)Since in diffeernt medium frequecy remains const

working model needed.........please help!!!!!!!!!!!!

A car is moving along a straight horizontal road at a speed of 20 meters per second.  The brakes are applied and a constant force of 5000 Newtons decelerates the car to a stop

Calculate the density of sodium metal. The length of the body-centered cubic unit cell is 4.24 A.


A tortoise can run with a speed of 0.12 m/s, and a hare can run 20 times as fast. In a race, they both start at the same time, but the hare stops to rest for 4.0 minutes. The torto

Why nuclear fission preceeds nuclear fusion?

list of anekardhi shabdh with examples

Fresnel''s diffraction due to a straight edge?

If the input voltage for the op amp shown in Figure, is -0.5V, Determine (a) The voltage gain (b) The output voltage.