Centripetal Motion Interactive

Exploring Centripetal Acceleration

In uniform circular motion, an object moves at constant speed but is constantly accelerating. How can this be? Explore these simulations to understand why acceleration doesn't just mean "speeding up" — it means any change in velocity, including direction.

🎯 Target Practice: Release to Hit the Target!

Score: 0 / 0
1.2x
How to Play: Press "Release!" when you think the object will travel toward the target. Which direction will it go when released? Try it and find out!

What Did You Notice?

  • Did the object fly outward from the center? Or did it go a different direction?
  • Key insight: Released objects travel tangent to the circle — NOT outward!
  • There is no "centrifugal force" pushing things out. That feeling is just your inertia!

Uniform Circular Motion: Velocity is Always Tangent

Velocity (v)
Centripetal acceleration (ac)
Radius
1.5 m/s
1.2 m
Current Values:
Speed |v| = 1.50 m/s  |  Centripetal Acceleration |ac| = 0.00 m/s²

Key Concepts

  • Velocity is always tangent to the circular path.
  • Acceleration points toward the center — this is centripetal acceleration.
  • v and ac are always perpendicular.
  • ac = v²/r  (Notice how the vectors change size with the sliders!)

Proving Centripetal Acceleration Points Toward Center

Circular Motion

Vector Subtraction: Δv = vf − vi

Step 1: The object moves clockwise. At position A, velocity vi is tangent to the circle.

The Mathematical Proof

a = Δv / Δt = (vf − vi) / Δt = (vf + (−vi)) / Δt

Even though |vi| = |vf| (same speed), the direction changes. Using tip-to-tail vector addition with vf + (−vi), the resultant Δv always points toward the center!