Uniform circular motion: speed and period
G2.5 G2.6 G2.7
By the end of this lesson you should be able to
- Describe the concept of uniform circular motion. G2.5
- Describe the concepts of average speed and period. G2.6
- Solve problems involving objects undergoing uniform circular motion at a constant speed using v = 2πr/T and a_c = v^2/r. G2.7
Key ideas
- Uniform circular motion: moving in a circle at constant speed.
- The period T is the time for one revolution; the frequency f = 1/T.
- Speed is constant but velocity is not: its direction is always tangent to the circle and keeps changing.
- If the inward force is removed, the object continues in a straight line along the tangent.
Key formulas (QCAA formula book notation)
\[
v = \frac{2\pi r}{T}
\]
\[
f = \frac{1}{T}
\]
Worked example
A merry-go-round of radius 2.5 m turns once every 6.0 s. Find the speed of a rider on the edge.
- \(v = 2\pi (2.5)/6.0 = 2.6\) m s⁻¹
Common mistakes
- Using diameter instead of radius.
- Saying an object at constant speed in a circle isn't accelerating.
Do
- Read: Textbook (Oxford Physics for Queensland Units 3 & 4) section 4.1-4.2
- Do: CYL 4.1 Q1, 4, 6; CYL 4.2 Q3
Try it
Watch
- Uniform Circular Motion: Crash Course Physics #7 · Crash Course
Further reading
- OpenStax College Physics 2e Ch. 6 Uniform circular motion and gravitation (OpenStax, CC BY 4.0)
- Full topic notes: Gravity & Motion