Centripetal Acceleration

Observe · predict · calculate · explain

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3D circular-motion laboratory

Real-world system

Radius5.0 m

Tangential speed8.0 m/s

Mass2.0 kg

Simulation speed1×

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Ready · 10 visual chapters.

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Learning objectives

Identify the inward direction of centripetal acceleration.
Distinguish tangent velocity from inward acceleration.
Apply aᶜ = v² ÷ r and aᶜ = ω²r.
Connect net inward force to real circular-motion systems.

Key ideas

Centripetal acceleration changes the direction of velocity and points toward the center. At fixed radius it grows with speed squared; at fixed speed it decreases as radius grows.

The required net inward force is mass times centripetal acceleration. Gravity, tension, friction, normal force, or contact forces may supply it.

Try these experiments

Double speed at fixed radius and compare acceleration.
Double radius at fixed speed.
Move a carousel rider outward at fixed angular speed.
Compare car, satellite, bucket, and rotor systems.
Generate a challenge and predict the arrows first.

Questions

Why can speed stay constant while velocity changes? Which real force points inward? Why does a high-speed tight turn require so much acceleration?

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Ten independent pages. Works with touch, stylus, mouse, Android devices and interactive smart boards.