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Chapter 3 — Chapter 3 — Circular and Rotational Motion
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Topic 1 of 6
📘Easy summary
If the length of an arc is equal to the radius of the circle, the angle subtended at the centre is one radian (rad), the SI unit of angle: θ = S/r, so S = rθ. 1 revolution = 2π rad = 360°, 1 rad = 57.3°. Angular displacement Δθ is the angle swept by a rotating line; positive for counter-clockwise rotation; for small values it is a vector along the axis given by the right hand rule (grasp the axis with fingers curling in the direction of rotation; thumb points along angular displacement). Angular velocity ω = Δθ/Δt (rad s⁻¹ or rpm). Angular acceleration α = Δω/Δt (rad s⁻²). Relations with linear quantities: v = rω and a = rα.
⭐Key points
- θ = S/r (radian).
- ω = Δθ/Δt; α = Δω/Δt.
- v = rω; a_t = rα.
🔬Diagram
🌿Real-life example
108 km h⁻¹ car, wheel r = 0.40 m: ω = 30/0.40 = 75 rad s⁻¹.
💡Exam tip
- Convert rpm to rad s⁻¹: × 2π/60.
✅Quick check
1. 1 radian is about:
2. v = ?
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