Physics HL · Chapter 2: Forces and Newton's Laws
2.5 Circular Motion and Centripetal Force
Connect changing velocity direction to centripetal acceleration and the inward net force requirement.
Estimated time: 30 minutes
Angular Speed, Period, and Linear Speed
In uniform circular motion, speed can stay constant while velocity changes continuously because direction rotates. The period T is time for one revolution, frequency f is revolutions per second, and angular speed ω tracks angular rate. Linear and angular descriptions are connected by v = rω.
These relationships let you translate between observation styles. If you know period and radius, you can obtain linear speed. If you know frequency, you can directly infer angular speed. Converting cleanly between forms often shortens calculations and prevents unit mistakes.
Why Constant Speed Still Means Acceleration
Acceleration is the rate of change of velocity vector, not speed alone. In circular motion, the velocity direction changes each moment, so acceleration exists even if speed is fixed. The acceleration points toward the center and has magnitude ac = v²/r, equivalently ac = ω²r.
Because acceleration is inward, net force must also be inward by Newton's second law. Any force source can provide this centripetal requirement: friction for a turning car, tension for a whirling mass, gravity for orbital motion, or normal force in track problems.
Identifying the Real Force Behind the Centripetal Effect
Centripetal force is not a new interaction type. It is the name for the net inward result. In each scenario, ask: which physical force points inward here? If friction is insufficient on a flat turn, the required inward net force is missing and the path radius increases, which appears as skidding outward.
Use the form that matches your given data to reduce algebra overhead.
Test Yourself
A 1000 kg car rounds a flat curve of radius 50 m at 10 m/s. What centripetal force magnitude is required?
Hint: Apply F = mv^2/r.