A ceiling fan with 28-in. blades rotates at 55 rpm.
(a) Find the angular speed of the fan in rad/min.

To find the angular speed of the fan in radians per minute (rad/min), follow these steps:

### Step 1: Convert the rotation speed to radians.
The fan rotates at 55 revolutions per minute (rpm). Each revolution corresponds to \( 2\pi \) radians. Therefore, the angular speed in radians per minute is given by:

\[
\text{Angular speed} = 55 \times 2\pi \text{ radians per minute}
\]

### Step 2: Calculate the angular speed.
\[
\text{Angular speed} = 55 \times 2\pi = 110\pi \text{ rad/min}
\]

### Step 3: Provide the final answer.
\[
\text{Angular speed} = 110\pi \text{ rad/min} \approx 345.58 \text{ rad/min}
\]

So, the angular speed of the fan is \( 110\pi \) rad/min or approximately 345.58 rad/min.

Would you like further details or have any questions?

Here are five related questions to consider:

1. How would the angular speed change if the fan's speed increased to 100 rpm?
2. What is the linear speed of the tip of the fan blades?
3. How would the angular speed be affected if the blade length changed to 36 inches?
4. How long does it take for the fan to complete one full revolution at this speed?
5. What is the relationship between linear speed and angular speed for the fan blades?

**Tip:** Remember that angular speed in rad/min is independent of the blade length; it only depends on the rpm.

Learn how to calculate the angular speed of a ceiling fan with 28-inch blades rotating at 55 rpm. Understand the conversion from rpm to radians per minute and how it relates to the fan's rotational speed. Suitable for high school students studying mechanics and angular motion.

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