Physics

The key insight is that a point farther from the axis travels a longer arc in the same time interval. Since angular speed $\omega$ describes how fast the angle changes (same for all points on a rigid object), you can connect it to linear speed $v$ by remembering that arc length equals radius times angle. This relationship reveals why the outer edge of a spinning disk moves faster than a point near the center, even though they rotate together.

The key insight is that a point farther from the axis travels a longer arc in the same time interval. Since angular speed $\omega$ describes how fast the angle changes (same for all points on a rigid object), you can connect it to linear speed $v$ by remembering that arc length equals radius times angle. This relationship reveals why the outer edge of a spinning disk moves faster than a point near the center, even though they rotate together.