Circular motion

Need to know

What you need to know

• **Radial (Centripetal) Acceleration:** Directed towards the centre of the circle. It changes the direction of the velocity. Its magnitude is $$a_r = \frac{v^2}{r} = r\omega^2$$.
• **Transverse (Tangential) Acceleration:** Directed along the tangent of the circle. It changes the magnitude of the velocity (the speed). Its magnitude is $$a_t = \frac{dv}{dt} = r\frac{d\omega}{dt}$$
• For **uniform circular motion**, the speed is constant, so the transverse acceleration is zero. The only acceleration is the centripetal acceleration.

Explanation

The Physics of Whirling

1. Draw a large, clear force diagram for the particle at a general point in its circular path.
2. Establish a coordinate system, typically with one axis pointing towards the centre of the circle (radial) and the other perpendicular to it (tangential).
3. Resolve all forces (like weight, tension, normal reaction) into components along these radial and tangential axes.
4. Apply Newton's Second Law (F=ma) to the radial direction: the sum of forces towards the centre equals mv²/r or mrω².