Question

The blades on a fan rotate at 750 revolutions per minute and have a diameter of 16 inches. Find the angular velocity of a fan blade and the linear speed of a point on the tip of the fan blade. Use 3.1416 as the value of pi.

Answer 1

Angular velocity
`\omega =` 78.5
`(rad)/(s)`

The value of liner speed of a point on the tip of the fan blade V = 16
`(m)/(s)`

Step-by-step explanation:

Given data

N = 750 R.P.M

D = 16 in = 0.4064 m

R = 0.2032 m

Angular velocity of a fan blade is given by

`\omega = (2 \pi N)/(60)`

Put all the values in above formula we get

`\omega = (2 (3.14)(750))/(60)`

`\omega =` 78.5
`(rad)/(s)`

The linear speed of a point on the tip of the fan blade is given by

V = R
`\omega`

V = 0.2032 × 78.5

V = 16
`(m)/(s)`

This is the value of liner speed.