Hello, I'm studying energy right now and I don't understand something: if we have a disk rolling without slipping, then obviously there is friction to induce the rolling right? So if we were to model this with an energy equation, would we have U + Wf = K where U is potential energy, Wf is work due to friction, and K is kinetic energy? OR would you have U = K + Kr where Kr is rotational energy? or some combination? Thanks!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
Total Mechanical Energy for Linear and Rotational Motion of a Solid:
ME = KE + RE + PE
= (1/2)mv^2 + (1/2)Iw^2 + mgh
did that help ?
Why can't you/don't you account for work done by friction?
No the friction from the rolling will cause it to stop. Roll a ball in a flat surface and it will eventual stop. The force that made it roll was the push.
If you are talking about a disk that is rolling down a ramp the force that is causing it to roll is gravity. At the top you have only potential and in the bottom you have kinetic.
There are more forces that affect the problem such as gravity and air resistance and its really hard to include all of them.
In cases or linear and rotational motion we only include gravity but in the real world if you measure the values its not going to match up because like you said there are other forces. So what you can do is use what you expect the energy to be using the formula that Mathmind posted and measure that actual results and use your equation to account for friction and all the other forces but then it gets complicated because you have to find by how much does kinetic affect the problem and as well as air drag.
The reasons we decide to exclude those forces is because they have minimal affect. I know you probably know that static friction has a big coefficient but as you go to rolling friction the coefficient goes to a very low number. That's why when people assume that rolling is causing a ball to continue to roll but it's actually a force acting apposite of it and causing it to stop.
Sorry this was long hope this helps.