Rotational Motion and Translational Motion are completely independent. However, for a point on the moving object, its individual motion may be more complicated,
One example of rotational and translational motion is a rolling cylinder. A point on the wheel may trace out a Cycloid over time.
When there is rolling without slipping:
- In terms of translational motion, every point of the wheel moves
. - In pure rotational motion, every point on the rim has translational motion
. At the bottom of the wheel, these two motions cancel out:
Meaning that:
This is a useful equation for different problems.
Because at the bottom of the wheel the velocity is zero, we can also think of the situation as the entire wheel rotating about the bottom.
