Motion in a Circle

Revise Motion in a Circle for Mechanics 3 WME03 (A2 Level) — revision notes and instant AI marking.

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Edexcel IAL Mechanics 3 (WME03)

Motion in a Circle

The big idea: Circular motion needs a resultant force towards the centre equal to mv²/r; in a vertical circle, energy links speeds at different heights.

Summary — What This Chapter Covers

Angular speed ω; v = rω.
Acceleration towards the centre: rω² = v²/r.
Conical pendulum: T cos θ = mg and T sin θ = mrω².
Vertical circle: use energy conservation plus the radial equation.

1. Angular Speed and Horizontal Circular Motion

Horizontal circles

Resolving vertically and radially

Resolve vertically (no vertical acceleration) and horizontally towards the centre (F = mrω²).

Worked Example

A 0.2 kg particle on a string of length 0.5 m moves as a conical pendulum with ω = 6 rad s⁻¹. Find the tension and the angle of the string to the vertical.

2. Motion in a Vertical Circle

Vertical circles

Energy and the radial equation

A particle on a string completes the circle only if the tension stays ≥ 0 at the top, which needs v² ≥ gr there. A particle on a rod (or inside a tube) only needs a speed ≥ 0 at the top.

String: complete circles ²

Memorise

Central acceleration

rω² = v²/r

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Motion in a Circle