Thank you for this video! I found this while trying to get a better grasp on Aristotle's Wheel Paradox (I kept seeing people mention "skidding") and while I'm still not 100% confident, I am definitely getting a better picture of the explanation. I think this also validated some of my suspicions that there is some "frame of reference" magic behind the wheel paradox, but I'm still noodling through it. I think I need to watch this again and your other videos to get a deeper understanding. Thanks again.
Grave mistake at 2:53-3:00, probably common among all physics learners since even an expert here is making it in a prepared lecture - It is false that every single point on the wheel has the same speed v_cm in rolling without slipping. For instance, the speed at the point of contact is 0, and the speed at the top point (north pole) is twice of v_cm, and it is possible (not hard) to compute the velocity (not just speed) of every single point in terms of the angle theta and distance r to the center using either trigonometry (law of cosine) or derivatives. Also it is more clear for the student to label the angle starting with the point of contact than the north pole so that the traced distance on the ground is easily identified with the arc length. - PK (A parent to a high school physics student)
Not sure it was a 'grave mistake', more a case of gradually introducing the concepts....the contact point being the instantaneous center of rotation (therefore having zero velocity) is covered in the very next video. Remember that these lectures have been parsed into very short 6-minute videos, it could be argued that this comes at some cost to continuity, but should be viewed with an eye towards the entire topic.
It was not a mistake... He just considered it as a case of translation and compared it with the case of rotation, that traversed the same distance and hence the same velocity.
Doubt: (For pure rolling motion) At the point of contact of the wheel at the ground , the net velocity=0 hence no motion. But if at that instant no motion is there then how can static friction act ? And if static friction does not act the net torque will also be zero , then how can the body continue the rolling motion ?
This is static friction, not kinetic. When static friction acts, there is never a motion. That's the point of static friction, to oppose forces trying to put a body into motion.
The position of the center of mass depends on the density distribution inside of the circle, but as there cannot be any mass outside of the circle which at the same time is part of the circle, there is no density distribution that shifts the center of mass outside the circle. It's possible to have a situation where the center of mass of the circle isn't exactly at the geometric center of the circle though, in which case you have to consider gravity to act on that point rather than the center of the circle.
well in this particular instance it's not important that the axis of rotation is goes through the center of mass, since we are just dealing with velocities and not momentum
See rolling without slipping means that the point touching the ground has zero velocity i.e, it is taking the ground with it and remember friction opposes relative motion ( in this case slipping) so the friction here becomes static (since no slipping) .if indeed there's slipping ( or skidding as u may imagine) friction becomes kinetic as u said.if u did not understand,that's fine ponder over it.it took a hella lot of time to get this clarity.😁
Doubt: (For pure rolling ) At the point of contact of the wheel at the ground , the net velocity=0 hence no motion. But if at that instant no motion is there then how can static friction act ? And if static friction does not act the net torque will also be zero , then how can the body continue the rolling motion ?
The velocity of the point in contact withe ground is zero relative to the ground, but not zero relative to the center of mass. If the wheel is rolling on a flat surface with V_cm = constant, then frition is zero. In that case the torque about the center of mass is zero, jence consant angular speed.
crystal clear. One of the best lectures on this topic
For everyone confused about how he writes backwards - do you realise how easy it is to mirror a video during editing. 😅
Man, this is explanation is too good.
Thank you for this video! I found this while trying to get a better grasp on Aristotle's Wheel Paradox (I kept seeing people mention "skidding") and while I'm still not 100% confident, I am definitely getting a better picture of the explanation. I think this also validated some of my suspicions that there is some "frame of reference" magic behind the wheel paradox, but I'm still noodling through it. I think I need to watch this again and your other videos to get a deeper understanding. Thanks again.
This man is a pro at writing backwards. Holy crap
They use special tech for the weird board and flip the video afterwards.
As a last-minute Highschooler who got recommended this video, I wish I could burn Physics completely.
Explanation is so concise and precise. Thanks !
5:55 This is not correct. NOT every point on the wheel has the same speed as the CM, as these speeds vary between 0 and 2Vcm
Mit is the best
Excellent explanation Sir.
Notice that he is writing in mirror image for viewers to see correctly
thanks you MIT falcuty
crystal clear！
rolling without slipping: 吃上劲了，转了也往前走了，转动和水平运动距离相等；slipping: 地上有冰，太滑了，原地转了但没往前走，或者转的比水平往前走的距离长；skidding: 没自转，直接站稳溜冰了，水平走的距离比转的长
Grave mistake at 2:53-3:00, probably common among all physics learners since even an expert here is making
it in a prepared lecture - It is false that every single point on the wheel has the same speed v_cm in rolling without slipping.
For instance, the speed at the point of contact is 0, and the speed at the top point (north pole) is twice of v_cm, and
it is possible (not hard) to compute the velocity (not just speed) of every single point in terms of the angle theta and
distance r to the center using either trigonometry (law of cosine) or derivatives.
Also it is more clear for the student to label the angle starting with the point of contact than the north pole so that
the traced distance on the ground is easily identified with the arc length.
- PK (A parent to a high school physics student)
Not sure it was a 'grave mistake', more a case of gradually introducing the concepts....the contact point being the instantaneous center of rotation (therefore having zero velocity) is covered in the very next video. Remember that these lectures have been parsed into very short 6-minute videos, it could be argued that this comes at some cost to continuity, but should be viewed with an eye towards the entire topic.
It was not a mistake... He just considered it as a case of translation and compared it with the case of rotation, that traversed the same distance and hence the same velocity.
Yes, I noticed he said for rolling without slipping, that all points are moving with the same speed v which is incorrect.
Thank you for this video🙏
Thanks a lot for the clear explanation!
When a cylinder goes down a slope and starts to slip what happens to the velocity of the cylinder?
I wonder what is the direction of friction force in 2. and 3. conditions.
Friction is in the direction to prevent slipping. So, it is to the right in case 2 and left in case 3.
Thank you so much!
A question faraway from the purpose of this video , how does he write like that ?
See lightboard.info to see how this was done.
this question kept me thinking through out the video now i have to rewatch
@@mitocw which book is best for this concept ( rolling friction)?
@@Azzu974 resnick halliday krane
ty very much sir
Doubt: (For pure rolling motion) At the point of contact of the wheel at the ground , the net velocity=0 hence no motion. But if at that instant no motion is there then how can static friction act ? And if static friction does not act the net torque will also be zero , then how can the body continue the rolling motion ?
This is static friction, not kinetic. When static friction acts, there is never a motion. That's the point of static friction, to oppose forces trying to put a body into motion.
What if the center of mass is not located at the center of the disc?
The position of the center of mass depends on the density distribution inside of the circle, but as there cannot be any mass outside of the circle which at the same time is part of the circle, there is no density distribution that shifts the center of mass outside the circle. It's possible to have a situation where the center of mass of the circle isn't exactly at the geometric center of the circle though, in which case you have to consider gravity to act on that point rather than the center of the circle.
well in this particular instance it's not important that the axis of rotation is goes through the center of mass, since we are just dealing with velocities and not momentum
Won't it be kinetic friction?
See rolling without slipping means that the point touching the ground has zero velocity i.e, it is taking the ground with it and remember friction opposes relative motion ( in this case slipping) so the friction here becomes static (since no slipping) .if indeed there's slipping ( or skidding as u may imagine) friction becomes kinetic as u said.if u did not understand,that's fine ponder over it.it took a hella lot of time to get this clarity.😁
This man just casually writing backwards
great...
Doubt: (For pure rolling
) At the point of contact of the wheel at the ground , the net velocity=0 hence no motion. But if at that instant no motion is there then how can static friction act ? And if static friction does not act the net torque will also be zero , then how can the body continue the rolling motion ?
The velocity of the point in contact withe ground is zero relative to the ground, but not zero relative to the center of mass. If the wheel is rolling on a flat surface with V_cm = constant, then frition is zero. In that case the torque about the center of mass is zero, jence consant angular speed.