A ceiling fan has 16inch blades so the radius of the circula

A ceiling fan has 16-inch blades (so the radius of the circular fan is 16 inches). Suppose the linear speed of the tip of a blade is 12 feet per second. (a) Find the angular speed of the fan in radians per minute. (b) Find the number of revolutions a blade makes per minute. Do not round any intermediate computations, and round your answer to the nearest whole number.

Solution

v = 12 feet /sec

radius = 16 inch = 16*0.0833 = 1.33 ft

a) angular spped = linear speed/radius = 12/1.33 = 9.02 rad/sec

= 541.35 rad/sec = 541 rad/sec

b) No. of rev per minute = angular speed /2pi = 86.159 = 86 rev/min