Question

The blades of a fan have a radius of 18.5 in. and they turn one revolution every 0.325 sec. Calculate the linear speed of the tip of a blade. Round to the nearest whole number

Answer 1

Linear Speed of a Rotating Particle

The linear speed is given by:

`v=\omega\mathrm{}r`

Where ω is the angular speed in radians/ seconds.

The angular speed can be calculated as a function of the number of turns (n) the particle had in a time (t):

`\omega=2\pi\cdot(n)/(t)`

We know the tip of the blade turns n = 1 revolution every t = 0.325 seconds, thus:

`\omega=2\pi\cdot(1)/(0.325s)`

Calculating:

ω = 19.333 rad/s

The speed for r = 18.5 in is:

`v=19.333\cdot18.5`

Calculating:

v = 358 in/s