An electric fan has blades of length `30 cm` as measured from the axis of rotation. If the fan is rotating at `1200 rpm`, find the acceleration of a point on the tip of a blade.

Explanation

To solve the problem, we need to find the acceleration of a point on the tip of a blade of an electric fan rotating at a certain speed. The steps to solve this problem are as follows:

### Step 1: Identify the given information
- Length of the fan blade (radius, \( r \)) = 30 cm = 0.3 m (converted to meters)
- Rotational speed of the fan = 1200 RPM (revolutions per minute)

### Step 2: Convert RPM to radians per second
To find the angular velocity (\( \omega \)), we need to convert the rotational speed from RPM to radians per second. The conversion is done using the formula:
\[ \omega = 2\pi f \]
where \( f \) is the frequency in revolutions per second. Since \( 1 \text{ RPM} = \frac{1}{60} \text{ RPS} \), we can convert:
\[ f = \frac{1200 \text{ RPM}}{60} = 20 \text{ RPS} \]
Now, substituting \( f \) into the formula for \( \omega \):
\[ \omega = 2\pi \times 20 = 40\pi \text{ radians/second} \]

### Step 3: Calculate the centripetal acceleration
The centripetal acceleration (\( a_c \)) at the tip of the blade can be calculated using the formula:
\[ a_c = \omega^2 r \]
Substituting the values we have:
\[ a_c = (40\pi)^2 \times 0.3 \]
Calculating \( (40\pi)^2 \):
\[ (40\pi)^2 = 1600\pi^2 \]
Now substituting this back into the equation for \( a_c \):
\[ a_c = 1600\pi^2 \times 0.3 = 480\pi^2 \text{ m/s}^2 \]

### Step 4: Final answer
Thus, the acceleration of a point on the tip of the blade is:
\[ a_c = 480\pi^2 \text{ m/s}^2 \]