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 of finding the acceleration of a point on the tip of a blade of an electric fan, we can follow these steps:

### Step 1: Convert the rotational speed from RPM to radians per second
The fan is rotating at 1200 revolutions per minute (RPM). To convert this to radians per second (rad/s), we use the conversion factor that 1 revolution is equal to \(2\pi\) radians and there are 60 seconds in a minute.

\[ \omega = 1200 \, \text{rpm} \times \frac{2\pi \, \text{radians}}{1 \, \text{revolution}} \times \frac{1 \, \text{minute}}{60 \, \text{seconds}} \]

Calculating this gives:

\[ \omega = 1200 \times \frac{2\pi}{60} = 40\pi \, \text{rad/s} \]

### Step 2: Identify the radius of rotation
The length of the fan blades is given as 30 cm. To use this in our calculations, we need to convert it to meters:

\[ R = 30 \, \text{cm} = 0.3 \, \text{m} \]

### Step 3: Calculate the centripetal acceleration
The formula for centripetal acceleration \(a\) at the tip of the blade is given by:

\[ a = \omega^2 R \]

Substituting the values we calculated:

\[ a = (40\pi)^2 \times 0.3 \]

### Step 4: Simplify the expression
Calculating \((40\pi)^2\):

\[ (40\pi)^2 = 1600\pi^2 \]

Now substituting this back into the acceleration formula:

\[ a = 1600\pi^2 \times 0.3 = 480\pi^2 \, \text{m/s}^2 \]

### Step 5: Approximate \(\pi^2\)
Using \(\pi^2 \approx 10\) for approximation:

\[ a \approx 480 \times 10 = 4800 \, \text{m/s}^2 \]

Thus, the acceleration of a point on the tip of the blade is approximately \(4800 \, \text{m/s}^2\).

### Final Answer:
The acceleration of a point on the tip of a blade is approximately \(4800 \, \text{m/s}^2\).

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