Angular and Linear Speed of a Wheel

Trigonometry · Axiom Academy

EXAMPLE Angular and Linear Speed of a Wheel Convert a wheel’s spin from rpm to rad/s, then use to find how fast a point on the rim travels. A bicycle wheel of radius turns at 100 revolutions per minute (rpm). Find the wheel’s angular speed in rad/s, then the linear speed v of a point on the tread. Nicely done — you turned a rotation rate into a real speed on the ground. rpm to rad/s: multiply revolutions per minute by (radians per revolution) and divide by 60 (seconds per minute). Angular speed: rad/s — how fast the wheel turns, shared by every point on it. Linear speed: m/s — how fast the tread actually moves. Same idea powers gears, CDs, and Ferris wheels: keep fixed and a larger radius always means a larger linear speed.

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