- #1
Is it a rule that I must start from heavy end?the density you used is defined from the lighter end and you have to find I about heavier end.
you may take the dx element at distance x from heavy end and then use (10-x) in the equation of density
It's not a rule, and it's not wrong to start at the light end. You may start anywhere you wish! But note that the problem is asking for the moment of inertia about the heavy end. Therefore, in the the calculation of the moment of inertia, the radial distances of the mass elements must be with respect to the heavy end. And be sure that the density at that distance from the heavy end is the correct density for that position along the rod.Is it a rule that I must start from heavy end?
Why it is wrong to start from light end?
Oh! Sorry for my carelessness, I didn't read the question carefully.It's not a rule, and it's not wrong to start at the light end. You may start anywhere you wish! But note that the problem is asking for the moment of inertia about the heavy end. Therefore, in the the calculation of the moment of inertia, the radial distances of the mass elements must be with respect to the heavy end. And be sure that the density at that distance from the heavy end is the correct density for that position along the rod.
I am so sorry that I don't understand.Suppose you break the integral into two. The first runs from x=0 to x= x_{cm}, the second from x_{cm} to 10. The density function remains as 2x + 4 for any value of x, so leave it alone. What is the distance from x_{cm} to the mass element in each case?
I am so sorry that I don't understand.
Can you explain it more clearly?:shy:
Do you mean this?
x is the position along the rod from the LHS. For the region to the left of the center of mass, the distance from the center of mass to x is x_{cm} - x. To the right of the center of mass, the distance is x - x_{cm}. The density at point x remains [itex] \rho (x) = 2 x + 4[/itex], since here x is always with respect to the light end of the rod.
You can set the center of mass at the origin if you translate the density equation accordingly for each section of the rod. Personally I tend to find it easier to leave the density function alone and work out the required distances as functions of the same x.Oh! It works and I get the answer!
But can you explain what's wrong with my method?
Why I can't set the center of mass as the orgin?
I use Visio to draw the pictures, then paste it into MS Paint to save it as a .gif type file.Work in #6 turns out to be correct, I just type it wrongly in my calculator.
By the way, how to generate the picture in #9?
What software are you using?