Physics

The key insight is that a point on a rotating object travels in a circle, and you can connect its linear (tangential) speed to how fast the whole object spins using the radius. Angular speed tells you how many radians the fan sweeps per second, while linear speed tells you how fast the tip moves along its circular path—they're related by a simple proportionality through the radius $r$.

The key insight is that a point on a rotating object travels in a circle, and you can connect its linear (tangential) speed to how fast the whole object spins using the radius. Angular speed tells you how many radians the fan sweeps per second, while linear speed tells you how fast the tip moves along its circular path—they're related by a simple proportionality through the radius $r$.