Question

A ceiling fan has
19
-inch blades (so the radius of the circular fan is
19
inches). Suppose the fan turns at a rate of
41
revolutions per minute.

(a) Find the angular speed of the fan in radians per minute.
(b) Find the linear speed of the tip of a blade in feet per second.

Do not round any intermediate computations, and round your answer to the nearest whole number.

Answer 1

1 revolution is \(2\pi\) radians.
41 revolutions per minute is \(41 * 2\pi\) radians / min = \(82\pi\) radians / min.

Answer 2

b) \(v = r\omega\)
r = 19 in. = 19/12 ft.
\(\omega = 82\pi\) radians per min = \(82\pi/60\) radians per second.
Find v.