Cool this is starting to come together. So one last question. The reason why engines aren't 100% efficient is because of this random factor? For example, the random movement of these atoms can't all be used to expand a piston, since some of that "work" will be put into changing the KEs of other...
Neat, thanks again for that comprehensive explanation.
So to sum it up, temperature is the measure of average translational KE, but, this is excluding the KE due to vibrations and rotations. In an adiabatic process, there is no gain in or loss in heat, then by definition there is no transfer...
To add on top of that, if heat is the transfer of KE through the collisions of atoms, why isn't it considered mechanical work? Aren't the atoms essentially doing work on other atoms?
Thank you for the clarification, so heat is just another method of energy transfer besides mechanical work.
Can you explain why does this occur? On the microscopic level, what exactly is happening to the atoms when there is a heat transfer? I always suspected the reason why heat flows from...
I have a dilemma, which has been nagging at me for a week.
So first off, can anyone verify my definitions are correct?
Heat is the flow of energy, and that flow is caused by the collisions of the atoms in a system. The collisions cause a transfer of KE, hence heat will flow from a substance...
Oh man! I understand now! It just clicked for me! I was looking at the expression the wrong way!
Thank you all for the help! This feeling of struggling to comprehend something then finally understanding it, it's just impalpable!
I've been receiving different responses that have been confusing me. I should've mentioned, my notion of using calculus may have been wrong. I forgot that dx represents a minute change, and the distance x is basically broken down to small elements of dx using the linear mass formula, as dm...
I actually read that page and it just added to my dilemma. From the diagram the distance for each xi is different, just as how the masses are different. So why is x represented as a constant in the integral?
The same goes for r2. Like Student100 mentioned, r is a constant and not the distance...
Okay, I think I found the solution to my dilemma. Since, the distance from each point mass is r distance away, hence, r is changing, but, the mass at each point is the same for a uniform rod. So we represent the small changes in mass by dm, so we can replace it with a density formula to...
A simple one would be a uniform rod. The method would involve ∫r2dm. However, I was confused as to why r2 is left as a constant. Since r is changing compared to where dm is, so shouldn't r also be represented as dr?
But, Student100 told me to just take the equation for what it is, since it...
The course just requires calc 2, or a coreq in calc 2. Currently I'm taking calc 2, so I guess I should just take this general formula as is?
However, I do plan to take mechanics, which requires multivariable, I guess that's where the proof for r2 will be explained?
That reminds me, my...
Oh, I don't know how I skipped your post.
I don't if I'm correct though, but, isn't that multivariable calculus? I'm still taking single variable at the moment. So I guess, dr is taken into consideration, but, I should just take the general formula as it is given?
Thanks for all your responses.
So generally, I = Σmiri2 = ∫r2dm
Why is the r2 left as a constant? Isn't it also changing depending on where the dm is located?
I asked this question to a physics major, and he said I should just take it as it is because I only know up to single variable...
When calculating the moment of inertia for a rotating object, why is "dr" not incorporated into the integral? However, dm is part of the integral, isn't the distance from the axis of rotation changing as well? Hence shouldn't the integral involve both dm and dr?