Question

A ceiling fan has 5-inch blades (so the radius of the circular fan is inches). Suppose the fan turns at a rate of 2 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 inches per minute.

Answer 1

Answer:

a) 12.56 rad per minute

b)62.8 inches per minute

Explanation:

Given:

• Radius of the blades, R=5 inches

• Frequency of the blades, f=2 revolutions per minute

a)

Let $\omega$ be the angular velocity of the blade which is given by

$\omega =2\pi f\\\omega=2\times 3.14 \times 2\\\omega=12.56\ \rm rad/min$

b)

Let v be the linear speed of the tip of the blade which is given by

$v=\omega \times R\\v=12.56\times 5\\v=62.8\ \rm inches/min$

Hence we have calculated the angular velocity and linear speed.