Hello, I have a doubt about inertia in a uniform bar and axis of rotation..
What's the difference between a lengthwise axis and a parallel one?
In some books I have found that when we're talking about lengthwise axis that pass through the center of the bar the inertia of the bar is equal to the inertia of a cylinder, and when it's about parallel axis that pass through the bar , the inertia is zero. I'm really confused with that words...
I'm not talking about the parallel axis theorem...
Thanks for any answer
https://www.physicsforums.com/threads/moment-of-inertia-of-a-rod-at-an-angle.449943/
If it passes through the bar along the axis of the bar, the moment of inertia is small because the mass is close to the axis of rotation. Remember that mR^2 stuff.
It is not zero though unless the radius of the bar is zero :) It is in fact a slender solid cylinder and its moment of inertia is
(1/2) mR^2
in the other direction, like spinning a baton about the center, it is much bigger
(1/12) m L^2
Note - L^2 is presumably HUGE compared to R^2
Hello! I can help explain the concept of inertia in relation to a uniform bar and different types of axes of rotation.
When we talk about a lengthwise axis of rotation, we are referring to an axis that passes through the center of the bar and is parallel to its length. In this case, the moment of inertia of the bar is equal to the moment of inertia of a cylinder with the same mass and length. The moment of inertia is a physical property of an object that describes its resistance to rotational motion. It depends on the object's mass distribution and the axis of rotation.
On the other hand, when we talk about a parallel axis of rotation, we are referring to an axis that can be any parallel line to the bar's length but does not pass through the bar itself. In some cases, like the one you mentioned, the moment of inertia of the bar with respect to a parallel axis passing through the bar is zero. This means that the bar has no resistance to rotational motion around that particular axis.
To understand why this happens, we need to consider the parallel axis theorem. It states that the moment of inertia of an object with respect to a parallel axis is equal to the sum of the moment of inertia of the object with respect to a central axis and the product of its mass and the square of the distance between the two axes. In this case, since the axis is passing through the bar itself, the distance between the axes is zero, so the moment of inertia around the parallel axis becomes zero too.
I hope this helps clarify the difference between a lengthwise axis and a parallel axis of rotation and why the moment of inertia of the bar behaves differently in these cases. If you have any further questions, feel free to ask!