Uniform circular motion (UCM) describes an object moving in a circular path at a constant speed. Due to its continuously changing direction, the object’s velocity is also constantly changing, resulting in centripetal acceleration that points towards the center of the circle.

What is Uniform Circular Motion?

Uniform circular motion (UCM) describes the movement of an object in a circular path at a constant speed.

Even though the speed is constant, the object’s velocity is constantly changing because its direction is always changing as it moves around the circle. Since velocity is a vector (magnitude + direction), a change in direction means a change in velocity.

And if velocity is changing, that means there must be acceleration!

Centripetal Acceleration

In UCM, the acceleration is called centripetal acceleration ($a_c$).

  • Direction: It always points towards the center of the circle. The word “centripetal” means “center-seeking.”
  • Magnitude: Its magnitude depends on the object’s speed ($v$) and the radius of the circle ($r$): \(a_c = \frac{v^2}{r}\)
  • Force: This acceleration is caused by a centripetal force (e.g., tension in a string, gravity for an orbiting satellite) that constantly pulls the object towards the center of the circle, preventing it from flying off in a straight line.

Interactive: Uniform Circular Motion

Observe an object moving in a circle. See its velocity and centripetal acceleration vectors change direction!

Uniform Circular Motion Simulator A simulation showing an object in uniform circular motion, displaying its velocity and centripetal acceleration vectors. Center V a_c Speed: 0.0 m/s Acc: 0.0 m/s²

Adjust speed and radius, then click "Play" to see uniform circular motion!

Why Uniform Circular Motion Matters

  • Planetary Orbits: Planets orbiting stars, and moons orbiting planets, are often approximated as uniform circular motion (or elliptical motion, which is a variation).
  • Engineering: Designing amusement park rides, centrifuges, or wheels on vehicles all involve principles of circular motion.
  • Everyday Life: From a car turning a corner to clothes spinning in a washing machine, UCM is all around us.

Interactive Match: Uniform Circular Motion

Test your understanding of key terms related to uniform circular motion.

Click a term and then its matching meaning. Match all pairs to complete!

Audio Explanation

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💡 Quick Concept Check:

An object is moving in a circle at a constant speed. Is its velocity constant? Is its acceleration constant? Explain.

Click to Reveal Answer
No, its velocity is **not constant** because its direction is continuously changing. No, its acceleration (centripetal acceleration) is **not constant** because its direction is continuously changing (always pointing towards the center), even though its magnitude might be constant.

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Practice Problems

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