Rolling Motion

If objects roll along the ground without slipping, then their translational and rotational quantities are related very simply:
```
  
                x  =  R * theta
       
                v  =  R * omega
       
                a  =  R * alpha
```
... as long as the angular quantities use radians (not degrees).

It is often necessary to cause different parts of the same machine to rotate at different speeds. Gears change one angular velocity to another; if they use teeth, then

     
          angular velocity of gear A         number of teeth in B
        -----------------------------   =   ----------------------
          angular velocity of gear B         number of teeth in A

Viewgraphs