Circular motion

For a particle on a circle of radius $r$: angular speed $\omega$ links to speed by $v = r\omega$.
The acceleration points to the centre — centripetal acceleration:

$$a = r\omega^2 = \frac{v^2}{r}$$

Horizontal circle: constant speed. Vertical circle: use energy conservation (speed changes with height).

Practice

A particle moves in a circle of radius 2 m with angular speed 3 rad/s. What is its speed v = rω (m/s)?

Practice

For the same particle (r = 2, ω = 3), what is the centripetal acceleration a = rω² (m/s²)?

Practice

The centripetal acceleration points:

You've got it

Key idea

$v = r\omega$; centripetal acceleration $a = r\omega^2 = \dfrac{v^2}{r}$, directed to the centre
horizontal circle → constant speed
vertical circle → use energy conservation