# Cart speed and wheel rotation

Say you have a horse drawn cart. Does the outside of the wheel spin at the same velocity that the cart moves forward?

The reason I ask is because I am working on a problem where a piece of mud detaches from the wheel when it is moving up, and then lands on the wheel again at the same spot. I don't see how this is even possible, though, if the cart moves forward at the same velocity that the wheel turns because some of the velocity in the mud will be in the y direction so it could never match the speed of the cart, much less beat it.

• This should probably be under homework and exercises. Some hints: 1. Velocity with respect to what? 2. Do all the parts of the wheel have the same velocity? 3. Think about the part of the wheel touching the ground - what must be its velocity with respect to the ground? Commented May 5, 2015 at 2:50
• I just provided the second paragraph for some context - but I guess it kind of turned into a question of its own. My real question is in the first sentence. Commented May 5, 2015 at 4:42
• A circular motion is not the same as a linear motion, so your question should say "is the velocity of the rim of the wheel the same as the velocity of the cart?" The bottom of the wheel does not move along the ground (otherwise it would slide or spin against the ground).
– LDC3
Commented May 5, 2015 at 5:38