Rolling Without Slipping Worked Example (kinematics, too) | Doc Physics

A ball rolls (without slipping) up a ramp and then launches into the air. Rotational dynamics and 2D kinematics are both discussed at length.

If you just want to hear how I really feel about America, skip directly to 21:13.

[victordolman]

We are privileged to listen in on this. This is reality, there is nothing polished or optimized about it. Students' knowledge and ability often leave room for improvement, not just desirable but essential improvement. Only they themselves can effect the necessary improvement. The teacher can help, facilitate, prod, stimulate, complain and ultimately praise, but his influence stops at the outside of the students' skull. Inside the student is king. Any improvement of the kingdom has to address the actual state of the kingdom.

It is soooo easy for a teacher to present the material efficiently, and make rapid 'progress' while never even noticing the intra-cranial chaos, and achieving very little in the way of student growth. Talking with students in the way of this video is excellent. Uncertainties, mistaken notions, downright confusion about what to do, sloppy reasoning, etc.: they all come out in the open, so that they can be addressed. I'm switching on my capslock now. IT DOES NOT MATTER HOW MUCH OR HOW LITTLE STUDENTS KNOW INITIALLY. What matters is that they are open and able to change, and learn what is needed. The ability to go forward is more important than the starting point, especially in Physics.

It can be quite scary to be open about your confusion about energy conservation or the exact meaning of rolling without slipping (I hate rolling without slipping, btw). I have seen situations in which students and teacher collude in a pretense that learning is taking place, simply out of fear of opening up. It is crucial that there is a high level of TRUST between students and teacher, so that students are not afraid to show mistakes and confusion. This video is a celebration of that trust. I loved it.

[reasons]

omg this is so easy compared to the Qs we get in our final exams, you guys are so lucky.

[thepianist]

This is a brilliant and rare video of a ball rolling up a ramp with and without friction. Bravo! The video did not give an answer to the last question: which V final is greater? I think the first ramp, because the ratio of rotational kinetic energy in the total kinetic energy is smaller, hence the translational kinetic energy is larger, which means the V is larger. Your reply is welcome!

[rajsondhi]

you deserve an A+. good job man keep it up

[TheIzugec]

Ah Doc I'm so glad that you're still doing videos, mostly for reason that chances are you will read this comment are bigger. I really wanted to thank you so much and  to write just how much this means to me.  I'm going through all the videos from ch 1  because I have finals in 2 months, and I love physics so much and i'll go to physics collage. I don't know if you are aware of it, but the way you teach physics is something that most of kids watching this have never experienced (including me) You have so much enthusiasm, and that's what I love about physics, you can really really love it up to level of yours :D To be honest, i got hooked up on physics one night when I watched something about quantum physics on youtube in second grade, and modern physics was always my cup of tea, and then I found myself watching your videos... aah, I'm so exited about you might seeing message that i don't even know what I wrote, just wanted to let you know that you succeed to make me and I believe many many people happy and we all appreciate it. 
Sincere regards from Croatia :)

[tear]

THE DOC IS BACK!!! But seriously, thank you so much for these videos... I have watched most of them.  I'm from the other side... I'm a literature major. But if I had seen your videos about 3 years early I would surely be a physics major :)

[victordolman]

Being me I cannot help wondering if the approach starting around 12:40 (breaking the parabolic motion into two parts: before and after the top) is the best way to go.

There necessarily are three main phases in solving such a problem: getting a clear view of the physical situation, identifying a promising approach, and carrying it through to the answer. At 12:40 we are at phase two. The top of the parabola is identified as a helpful notion to make the problem more tractable by splitting it into two simpler parts. But do we gain all that much in simplicity? We still need to deal with the quadratic term for the vertical motion in both parts. The only thing we avoid is the weird second solution at negative x, which we would get if we did not slit the problem. Mwah, not much to show for our increased effort.

Here is how I learned it forty years ago from Mr. Elderenbosch. After the ball is launched we decompose its motion into horizontal and vertical components. We identify the horizontal motion as uniform and the vertical motion as uniformly accelerated. Then the entire class would chant the equation for the position in case of uniform motion:

x = vx0 t + x0.

Yes, Elderenboch would actually have us say this out loud in unison. Same for the uniformly accelerated motion in the y-direction:

y = (1/2) g t^2 + vy0 t + y0.

He could hear if someone got it wrong or did not join in. Then he would say: "Toe nu, klas!" and we would raise our voices slightly and say the formula.

Then we list all the things we know, similar to what you do: g=9, 81m/s^2, x0=0 by choice, y0=3m, vx0=v0*cos(25deg), vy0=v0sin(25deg), and v0=7, 61m/s from the previous exercise. (Nice detail: note the Dutch decimal comma's instead of the American decimal points.) That leaves us with unknowns: x, y and t. Now what? We want to find x when the ball hits the ground, i.e. when y=0. Put that in. So we end up with two equations with two unknowns: x and t. We don't care about t at all, so we have to eliminate it. This indeed looks promising. Now we are ready for phase three: do the math. It is straightforward, except for the part where we get two solutions and have to reject the one with negative x.

Of course we previously had spent ages talking about uniform and uniformly accelerated motion and their equations, so they were ready repertoire.

Your approach is slightly different. Your students' repertoire is slightly different, and it seems that they need to look harder for a viable approach. You are less pompous about the decomposition and naming the motions. But most importantly, you go for the intermediary step of considering the top of the parabola. You also have the sign ambiguity when taking the sqroot, but you can gloss over it easily. On the whole I feel that the intermediary step does not help the students who are already hesitant and insecure, and that the way of Mr. E is more helpful in keeping a clear view. (And I loved the chanting.)

[maryamhashem]

Hi Doc! For the last question, will the ball in the second scenario have a greater launch velocity?? Thanks!

[zzmfgz]

I'm skeptical about your first answer. Is it only an approximation? I believe when the ball reaches the top of the incline it will rotate about the corner and fall off when it's center off mass is less than 3m above where it started (thus the final velocity you calculated is a bit too small).

[mkiss]

Where's the rest of the problem solution? I enjoyed this one.

[YourAverageHater]

so these are the minds im competing with, awesome

[davidloop]

in the last section, for the frictionless ramp, u said that the initial Krot = final Krot = 500J, I thought some of the initial Krot will be turned into gravitational potential energy at the top of the ramp, so initial Krot will not be equal to final Krot

[kausiksivakumar]

how do you know that the time 0.32 sec will be required for the ball to come to the point in the parabola where v(y)=0 why wont that be the time the sphere reaches the ground ( coz v(y) =0 there)

[dougb]

Hi Doc,

the solution present to the first problem is close, but not not quite accurate.  I'm referring to the fact that at the point when the sphere launches from the top of the ramp, the center of mass of the sphere is still slightly behind and below the point you assume in your analysis.  Have you heard this before, or should I elaborate?

-Doug.

[naeemghafori]

sir, why we are not considering the angle while it leaves the top ??

[cyrusIIIII]

I did not understand the part about friction! how is that possible to have static friction and no kinetic friction? How is that possible to roll without friction?

[kausiksivakumar]

how do you know that 2/7 th of energy will be rotational?

[MASTERable]

Understood everything but the part at the end where wi=wf if friction is 0. Why is the wi = wf if there is no friction? In the second case, since the ramp is frictionless, isn't the ball SLIDING up the ramp since there's no friction to cause it to roll? If it's sliding up the ramp, isn't it true that it has no rotational motion and so isn't wf=o because the ball is not rolling but rather sliding up the ramp??

[ENSN]

what on earth is a "sqweer" and "thuuur", x'D