I've been having trouble with this topic for a while now. I've re-read the section dozens of times now, but I'm still not exactly clear and I was hoping for clarification on a couple of things.(adsbygoogle = window.adsbygoogle || []).push({});

In a system of particles, I can see intuitively how the velocity of a particular particle will be the sum of the velocity of the center of mass and the velocity of the particle relative to the center of mass.

To pick an example, a tire of the moving car will have both translational and rotational motion.

Here's a picture to illustrate what I wrote below:

http://i.imgur.com/0PxxLod.png

I represent the translational velocity of the entire tire by the velocity of the center of mass, so each and every particle has the same linear velocity.

The angular velocity depends on the position of the particle.

If there's rolling without slipping, the bottom particle must be at rest. The only way for this to happen with vector addition is for the magnitude of the angular velocity at the bottom to be equal in magnitude of the linear velocity vector but opposite in direction. Since the angular velocity is constant in magnitude but changing in direction by position, the actual velocity of each particle is the vector sum of the linear velocity of the center of mass plus the particle's respective angular velocity vector and the top particle's velocity is twice as fast as the velocity of the center of mass.

Assuming all of the above is correct, here's where my confusion begins...

If the bottom particle is at rest, then there can be no kinetic friction and there's only static friction.

Assuming that the tire is perfectly circular and the surface is perfect (not bumpy) does this mean that friction does no work in the movement of the tire? If the bottom particle has zero velocity, it isn't moving and can't be doing any work.

Does the slipperiness of a surface come into play? I'm assuming kinetic friction won't matter, but will the coefficient of static friction be relevant?

Also, if the wheel is at rest when it comes into contact with the surface, how does the wheel even make a displacement? What stops it from just... spinning around in place? I'm just finding it very unintuitive.

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# Rolling without slipping

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