Question

The blades on a ceiling fan spin at 60 rotation per minute as shown in the figure below. The fan has a radius of 50cm.Calculate the linear speed of a point at the outer edge of a blade in meter per second.

Answer 1

Answer on Question #42239, Physics, Mechanics | Kinematics | Dynamics

The blades on a ceiling fan spin at 60 rotation per minute as shown in the figure below. The fan has a radius of 50cm. Calculate the linear speed of a point at the outer edge of a blade in meter per second.

60 rotations per minute

Solution:

Given:

$$\begin{array}{l} f = 60 \mathrm{rpm}, \\ R = 50 \mathrm{cm} = 0.5 \mathrm{m}, \\ v = ? \end{array}$$

Rotations per minute (abbreviated rpm) are a measure of the frequency of a rotation. It annotates the number of turns completed in one minute around a fixed axis.

We have

$$f = 60 \mathrm{rpm} = \frac{60 \text{ rotation}}{60 \mathrm{s}} = 1 \mathrm{Hz}$$

Linear speed = radius × angular speed

$$v = R \omega$$

The conversion between a frequency $f$ measured in hertz and an angular speed $\omega$ measured in radians per second are:

$$\omega = 2 \pi f$$

Thus,

$$v = R \omega = 2 \pi f R = 2 \cdot 3.14 \cdot 1 \cdot 0.5 = 3.14 \mathrm{m/s}$$

Answer. $v = 3.14 \mathrm{m/s}$

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