Circular Motion

Revise Circular Motion for Physics 4 (IAL) WPH14 (A2 Level) — revision notes and instant AI marking.

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Edexcel IAL Physics — Unit 4

Circular Motion

The Big Idea Anything moving in a circle at constant speed is still accelerating — because its keeps changing — and something must always be pulling it toward the centre to keep it there.

Quick Summary

Radians measure angles using arc length ÷ radius — they're the "natural" unit for anything going in circles.
Angular displacement (Δθ) is how far round the circle something has swept, in radians.
Angular velocity (ω) is how fast that angle changes — the rotational equivalent of linear velocity.
Even at constant , an object going in a circle is always accelerating, because velocity is a vector and direction is constantly changing.
This acceleration is called centripetal acceleration — always pointing toward the centre of the circle.
Newton's Second Law says acceleration needs a force — that resultant force is the centripetal force, also always pointing toward the centre.
Centripetal force isn't a new type of force — it's whatever existing force (tension, friction, gravity...) happens to be doing the job of keeping the object curving.
In vertical circular motion, tension/normal force varies around the loop because gravity adds to it at the top and subtracts from it at the bottom (or vice versa depending on setup).

Topic 1 — Radians & Angular Displacement

What actually is a radian?

You're used to measuring angles in degrees, where a full circle is 360°. That number is completely arbitrary — it comes from ancient Babylonian counting systems, not from anything physical about circles. Radians, on the other hand, are defined , which is exactly why physicists love them for circular motion.

Here's the definition: one radian is the angle you get at the centre of a circle when the arc (the curved distance around the edge) is exactly as long as the radius. Imagine taking a piece of string the same length as the radius, laying it along the curved edge of the circle, and then drawing two lines from its ends back to the centre. The angle between those two lines is 1 radian — roughly 57.3°.

Because the full circumference of a circle is 2πr, and each "radius-length" of arc corresponds to 1 radian, a complete circle (360°) is exactly 2π radians (≈ 6.28 rad). That's not a coincidence you need to memorise separately — it falls straight out of the definition.

Angular Displacement

Δθ = Δs / r

Δθ = angular displacement (radians)
Δs = arc length / distance travelled around the circle (m)
r = radius of the circle (m)

In plain words: angular displacement is just "how much arc did you cover, relative to the size of the circle." A bigger circle needs a longer arc to sweep out the same angle.

Converting Between Degrees and Radians

Since 360° = 2π rad, to go from degrees to radians: θ° × (π/180) = θ rad. To go the other way: θ rad × (180/π) = θ°. Common ones worth knowing cold: 90° = π/2, 180° = π, 270° = 3π/2, 360° = 2π.

Calculator Trap

Practice Question

An angle is given as θ = π/3 radians. What is this in degrees?

Practice Question

Topic 2 — Angular Velocity