Suppose a circular object is rolling along a straight line. I seem to have seem vaguely that tangential velocity of the point of contact is equal to the velocity of center of mass(or that sort of things i am not really sure).What does the velocity of point of contact has anything to do with center of mass? I see that this is a concept which i haven't been taught in my school books. I would like to learn more about this concept. So could the physics lovers kindly explain this concept intuitively or provide some sources where i could learn them?It would be a great help to me.
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4 Answers
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I made some animations for you.
The center of mass is the blue dot. When the cylinder is on a slippery floor, imagine it on an ice sheet, the point of contact (red) could just slide and no rotation on the cylinder occurs. Both dots travel at the same speed.
But if the cylinder is really rolling the initial point of contact is now orbiting the center of mass.
And it describes an interesting pattern.
Let me now turn the camera to a top view, so you can clearly see the acceleration and deceleration pattern. I faded out the cylinder so you can focus on the initial line of contact.
You can clearly see that when the point of contact is again on the floor, the speed relative to the floor is zero.
Just to complement, here is a lateral view, so you also can see the vertical velocity.
In general, the speed of the red dot does depend on the speed of the center of mass, but on the specific moment the line is on contact to the floor, the speed is 0.
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If your round object is rolling (and not sliding) then the velocity (relative to the surface) at the point of contact is zero. The velocity of the object (relative to the surface) is defined by the motion of the center of mass. The speed of the point of contact (relative to the center) is the same as the speed of the center (relative to the surface), but in the opposite direction. The speed of the top of the object (relative to the center) is the same as at the bottom (but in the forward direction).
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For an observer in the frame of the ground, the velocity of the point of contact with the ground is zero if there is no slip. It is easier to understand if we move to the roll's axis frame. In this case the ground is being "moved" by the roll, and of course with the tangential speed of the roll. If velocities are the same in this frame, it must be the same for the ground's frame. As the velocity of the ground is zero for someone there at rest, the velocity of the point of contact must be also zero.
If in the roll's axis frame, the velocity of a point at the periphery is $v$, that is the same "velocity" of the ground, then in the frame of the ground, the velocity of the roll's axis must be $-v$.
answered Sep 12, 2021 at 22:33
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If the circle is really rolling, you have no velocity at the point of contact. And this has nothing to do with the center of mass. the top point of the circle moves wth twice the velocity of the center.Just take any round thing like a round plate and try it out. Many things are easier to understand by doing an experiment!
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$\begingroup$ Thanks for the reply but could you please explain why there is no velocity at the point of contact theoretically?And as for the COM thing,here is a link which relates with COM but i didn't understand the post fully physics.stackexchange.com/questions/64555/… $\endgroup$– madnessCommented Sep 12, 2021 at 16:48
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$\begingroup$ If you had a velocity at the point of contact, the thing would not roll but slip. so the velocity of the contact point is the slip velocity, thats why wrote " if it is really rolling" Why did you not try it out. ? $\endgroup$– trulaCommented Sep 13, 2021 at 10:20