Circular Motion Core Concepts

Definition

Circular motion is motion along the circumference of a circle or circular arc. Even if speed is constant, velocity changes because its direction changes continuously.

Why It Matters

Circular motion problems require students to connect linear motion along the path with angular motion about the centre. The first task is always to identify the radius, the centre of the circular path, and the direction of the instantaneous velocity.

Key Representations

Angular displacement in radians:

$$\theta =\frac{s}{r}$$

Arc length:

$$s=r\theta$$

Angular velocity:

$$\omega =\frac{\Delta \theta }{\Delta t}$$

For uniform circular motion:

$$\omega =\frac{2\pi }{T}=2\pi f$$

Tangential speed:

$$v=r\omega$$

Notes

• Velocity is tangential to the circular path.
• Angular quantities describe the angle swept out at the centre.
• Radian measure must be used in $s=r\theta$ and $v=r\omega$.
• Uniform circular motion has constant speed but changing velocity.
• Non-uniform circular motion has changing speed and therefore has both radial and tangential acceleration.
• Constant speed does not mean zero acceleration.

Links

• Related: circular motion
• Related: non uniform circular motion
• Related: vectors
• Related: Dimensionless Quantities
• Misconception: vector direction consistency