A.2.26—Angular and linear speed

Connect the descriptions

For uniform circular motion,

$$v=\frac{2\pi r}{T}=\omega r$$

Angular speed $\omega$ is the same for all points on a rigid rotating body, while linear speed increases with distance from the axis.

Use the period

One revolution takes period $T$, so $\omega=2\pi/T$. Keep radians and seconds consistent.

Compare points on one disk

If one point is twice as far from the centre, its linear speed is twice as large at the same angular speed; its centripetal acceleration is also twice as large.

Common trap

Do not assume equal linear speeds for all points on a rotating disk. Equal angular speed does not mean equal tangential speed.