Trigonometry: Velocity of belt driving a pulley

I've got this Situation in our trigonometry class and i'm a bit confused.. Here is the math problem: A pulley of radius 6 inches drives a machine by a belt. If the pulley is turning at 300 rev/min, what is the velocity of the belt in feet per minute? Kindly answer with solution, please..

Jhun Vert's picture

There is a direct formula to convert rotational velocity to tangential velocity, it is given by v = rω, where v = linear velocity, r = radius of the circle, ω = angular velocity in radian / unit of time.

v = 0.5 (300 × 2π)

v = 300π ft/min       answer

The length of belt that pass through every one revolution is equal to the circumference of the pulley, in this case, circumference of pulley = 2πr = 12π inches. For 300 revolution, it will be 300 × 12π = 3600π inches or 300π ft.

Thank you so much for the explanation..

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