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📘 Lesson 8 of 19 · Mechanics

🔄 Circular Motion

An object moving in a circle is constantly changing direction, even at constant speed — this requires a special kind of acceleration and force pointed toward the circle's center.

Course progress: 42%

01 Key Concepts

Uniform Circular Motion

Motion in a circle at constant speed; even though speed doesn't change, velocity does (since direction is always changing).

Centripetal Acceleration

The acceleration directed toward the center of the circle, required to keep an object moving in a circular path: a_c = v^2/r.

Centripetal Force

The net force directed toward the center that causes centripetal acceleration: F_c = m*v^2/r. This isn't a new type of force -- it's whatever force (tension, gravity, friction) happens to point inward.

Period and Frequency

Period (T) is the time for one full revolution; frequency (f) is the number of revolutions per second; they're related by f = 1/T.

Angular Velocity

The rate of change of angle over time, omega = 2*pi/T (in radians per second), related to linear speed by v = omega*r.

02 Key Formulas

03 Solved Examples

Example 1 A car moves at 20 m/s around a curve with radius 40m. Find its centripetal acceleration.
  1. Apply a_c = v^2/r = 20^2/40 = 400/40.
Answer: 10 m/s^2
Example 2 A 2 kg ball moves in a circle of radius 0.5m at 4 m/s. Find the centripetal force required.
  1. Apply F_c = m*v^2/r = 2*4^2/0.5 = 2*16/0.5.
  2. = 32/0.5.
Answer: 64 N
Example 3 An object completes one revolution every 4 seconds. Find its angular velocity.
  1. Apply omega = 2*pi/T = 2*pi/4.
Answer: omega = pi/2 radians/second (approximately 1.57 rad/s)

04 Practice Questions

1A car moves at 10 m/s around a curve of radius 25m. Find centripetal acceleration.
4 m/s^2
2A 1 kg ball moves in a circle of radius 2m at 6 m/s. Find centripetal force.
18 N
3An object has period 2s. Find its frequency.
0.5 Hz
4What direction does centripetal acceleration always point?
Toward the center of the circle
5Is centripetal force a new, separate type of force?
No, it's whatever existing force (tension, gravity, friction, etc.) happens to point toward the center

📄 Circular Motion — Downloadable Worksheet

10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.

🗒 Cheat Sheet ⬇ Download PDF 🖥 Interactive Worksheet