Circular Motion: Complete A Level H2 Physics Cheatsheet
A Level Physics (H2), Chapter 7 · 9478 Topic 7 · Read time: ~9 minutes
These notes come from TGC Academy's A Level H2 Physics tuition in Singapore. Checking your rank points? Try our free RP calculator.
Key Formulas
Radians and angular velocity
One radian is the angle subtended at the centre of a circle by an arc equal in length to the radius. θ (rad) = arc length ÷ radius.
Angular velocity (ω) is the rate of change of angular displacement, in rad s⁻¹. For one full revolution, ω = 2π/T.
Every point on a rotating rigid body has the same ω, but points further out have a larger linear speed, v = rω.
Trap: Set your calculator to radians whenever ω or θ appear in rad. A degree-mode calculator gives wrong answers with no warning.
Centripetal acceleration
In uniform circular motion the speed is constant but the velocity's direction keeps changing, so the body is accelerating.
This centripetal acceleration points towards the centre: a = v²/r = rω².
Motion along any curved arc needs a resultant force that is perpendicular to the velocity and points towards the centre of curvature. Because it is perpendicular to the motion, it does no work and the speed does not change.
Centripetal force is not an extra force
Centripetal force is the name for the resultant force towards the centre, F = mv²/r. It is supplied by real forces already present: tension in a string, friction on a car's tyres, the normal force on a loop, or gravity on a satellite.
Method: draw the real forces, find their resultant towards the centre, then set it equal to mv²/r.
Trick: In a vertical circle on a string, tension is largest at the bottom (T − mg = mv²/r) and smallest at the top (T + mg = mv²/r). The minimum speed at the top is when T = 0, giving v = √(gr).
Trap: Never draw an extra 'centripetal force' arrow on a free body diagram. It is the result of the forces already there, and adding it double counts.
Worked Example
A 0.50 kg mass on a 0.80 m string is whirled in a vertical circle. At the lowest point its speed is 6.0 m s⁻¹. Take g = 9.81 m s⁻².
(a) Calculate the angular velocity at the lowest point. [1]
ω = v / r = 6.0 ÷ 0.80 = 7.5 rad s⁻¹
(b) Calculate the centripetal acceleration at the lowest point. [1]
a = v² / r = 36 ÷ 0.80 = 45 m s⁻²
(c) Calculate the tension in the string at the lowest point. [2]
Resultant force towards centre (upwards): T − mg = ma
T = 0.50 × 45 + 0.50 × 9.81 = 22.5 + 4.9 = 27.4 N
Why this question is a good test of the topic: part (c) is where the common mistake shows up. Tension is not just mv²/r, because weight acts in the opposite direction at the bottom and tension must overcome it as well.
Frequently Asked Questions
What is a radian?
The angle at the centre of a circle subtended by an arc equal in length to the radius. 2π radians = 360°.
Is an object moving in a circle at constant speed accelerating?
Yes. Its direction keeps changing, so its velocity changes. The acceleration points towards the centre.
Is centripetal force a separate force?
No. It is the resultant of the real forces acting, such as tension, friction or gravity, that points towards the centre.
Why doesn't the centripetal force change the speed?
It acts perpendicular to the velocity, so it does no work and only changes the direction of motion.
Where is the tension greatest in a vertical circle?
At the bottom, where tension must provide the centripetal force and also overcome the weight.
Still adding centripetal force to your diagrams?
Small group A Level H2 Physics classes at TGC Academy's Bishan, Bukit Timah and Potong Pasir centres, helmed by Andrew Seah, MOE Award-Winning Teacher and Marshall Cavendish textbook author, with a team of tutors.