Moment of inertia - disk - finding dm

In summary, a user is asking for help with finding the moment of inertia with respect to various axis. They are having trouble figuring out how to find the element of mass, dm, which is equal to (rho)*t*dA. They tried using t*dA = (pi)(r^2)/2 but it did not work. They provide a picture of a disk and ask for help slicing it up for integration. After no replies for 24 hours, they figure it out on their own.
  • #1
O011235813
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hey, I am trying to figure out the moment of inertia with respect to various axis. I am, having trouble figuring out how to find out dm.
I know that dm = (rho)*t*dA, but i am having trouble figuring out the t*dA part. i tried using

t*dA = (pi)(r^2)/2
That didn't work. If some1 could help me figure this out i'd be much grateful.

Here is the picture of the disk

[URL=http://img165.imageshack.us/my.php?image=semidiskad3.png][PLAIN]http://img165.imageshack.us/img165/6294/semidiskad3.png[/URL] http://g.imageshack.us/img165/semidiskad3.png/1/ [/PLAIN]
 
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  • #2
Hi O011235813! :smile:
O011235813 said:
hey, I am trying to figure out the moment of inertia with respect to various axis. I am, having trouble figuring out how to find out dm.
I know that dm = (rho)*t*dA, but i am having trouble figuring out the t*dA part. i tried using

t*dA = (pi)(r^2)/2
That didn't work. If some1 could help me figure this out i'd be much grateful.

hmm … no replies in almost 24 hours …

so I'm guessing everyone's as confused as I am :confused:

dm is an element of mass, and rho is density, but what are t and dA supposed to be, what shape volume are you considering (the diagram doesn't make it clear), about which axis, and how are you trying to "slice up" this volume for integration?
 
  • #3
hey,

yeah sorry for the confusing. I figured it out so I'm good now. Thanks for replying back though :D
 

1. What is moment of inertia and why is it important?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is important because it helps us understand how objects behave when they are rotating and how much force is needed to change their rotation.

2. How is moment of inertia calculated for a disk?

Moment of inertia for a disk can be calculated using the formula I = (1/2) * m * r^2, where m is the mass of the disk and r is the radius of the disk.

3. What is the significance of finding "dm" in the moment of inertia formula for a disk?

The "dm" in the moment of inertia formula represents the infinitesimal mass elements that make up the disk. It is important because it allows us to take into account the distribution of mass within the disk, which can affect its moment of inertia.

4. How does the moment of inertia change for a disk when its mass or radius is increased?

If the mass of a disk is increased, its moment of inertia also increases. This is because there is more mass to resist changes in rotation. Similarly, if the radius of a disk is increased, its moment of inertia also increases as there is more distance from the axis of rotation for the mass to be distributed.

5. How is the moment of inertia of a disk related to its angular velocity and angular acceleration?

The moment of inertia of a disk is directly proportional to both its angular velocity and angular acceleration. This means that as the disk's angular velocity or acceleration increases, its moment of inertia also increases, making it more difficult to change its rotational motion.

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