How fast will a robot drive? It depends on how fast its wheels turn and how big they are.
Key idea
A wheel that rolls without slipping moves at $v = \omega r$, where $\omega$ is its angular speed in radians per second and $r$ its radius. To change rpm to rad/s, multiply by $2\pi/60$.
Why it works
In one turn the wheel's rim lays down its whole circumference, $2\pi r$, on the floor. So turns per second times $2\pi r$ is the speed, which is the same as $\omega r$.
Worked example: Robot speed
A 6.5 cm wheel (radius 3.25 cm) turns at 120 rpm.
- $\omega = 120 \times 2\pi / 60 \approx 12.57\ \text{rad/s}$.
- $v = 12.57 \times 0.0325 \approx 0.41\ \text{m/s}$.
Answer: About 0.41 m/s.
Common mistake
Multiplying rpm by the radius without changing to radians per second. The answer comes out about 10 times too big.