Same Spin, Different Speeds

You'll learnthat riders on one spinning body share angular speed but not linear speed.

Two riders on one carousel finish every lap together — and one of them is moving four times as fast. The radius is the exchange rate between the spin they share and the speed they don’t.

8 STEPS · 6 QUICK CHECKS · v5

ROTATION LAB

Before you start

What you're looking at

A carousel turning steadily at 3 rad/s with a hub rider 0.5 m from center and a rim rider 2.0 m out, on the same spoke.

The question

They finish every lap together, but are they moving at the same speed?

Watch for

The angle wedge growing identically for both riders while their linear speeds pull apart; predict who moves faster.

What the symbols mean

The two riders are color-tagged (hub and rim); the ω line marks the shared angular velocity; radius is the exchange rate to speed.

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