**Problem 6:** A ceiling fan turns at a rate of 20 RPM. What is its speed in radians per second, and the speed of the tip of a 50 cm fan blade in m/s?**Explanation:**- **Converting RPM to radians per second:** - RPM (revolutions per minute) can be converted to radians per second by using the conversion factor: \[ 1 \text{ revolution} = 2\pi \text{ radians} \] - Therefore, \[ \text{Speed in rad/s} = \text{RPM} \times \frac{2\pi}{60} \]- **Calculating the speed of the tip of the blade:** - The speed (v) of the tip of the fan blade in m/s can be calculated using the formula: \[ v = \omega \cdot r \] - where \(\omega\) is the angular speed in radians per second and \(r\) is the radius (length of the fan blade in meters).These calculations help in understanding the rotational dynamics of objects like ceiling fans.

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Answered: 6. A ceiling fan turns at a rate of 20…

6. A ceiling fan turns at a rate of 20 RPM what is its speed in radians per second, and the speed of a tip of a 50 cm fan blade in m/s?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Torque

Torque is the rotational equivalent of linear force in physics and mechanics. Based on the course of study, it is also known as the moment of force, rotational force, or turning effect.

Question

**Problem 6:** A ceiling fan turns at a rate of 20 RPM. What is its speed in radians per second, and the speed of the tip of a 50 cm fan blade in m/s?

**Explanation:**

- **Converting RPM to radians per second:**
- RPM (revolutions per minute) can be converted to radians per second by using the conversion factor:
\[ 1 \text{ revolution} = 2\pi \text{ radians} \]
- Therefore, \[ \text{Speed in rad/s} = \text{RPM} \times \frac{2\pi}{60} \]

- **Calculating the speed of the tip of the blade:**
- The speed (v) of the tip of the fan blade in m/s can be calculated using the formula:
\[ v = \omega \cdot r \]
- where \(\omega\) is the angular speed in radians per second and \(r\) is the radius (length of the fan blade in meters).

These calculations help in understanding the rotational dynamics of objects like ceiling fans.

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