A wheel rotates with a constant angular velocity of 300 rpm. The angle through which the wheel rotates in 1 s is.

Options

A. `pi` rad
B. `5 pi` rad
C. `10 pi` rad
D. `20 pi` rad

Explanation

To solve the problem of finding the angle through which a wheel rotates in 1 second given its angular velocity of 300 rpm, we can follow these steps:

### Step 1: Convert Angular Velocity from RPM to Revolutions per Second
The given angular velocity is 300 revolutions per minute (rpm). To convert this to revolutions per second (rps), we divide by 60 (since there are 60 seconds in a minute).

\[ \text{Angular velocity in rps} = \frac{300 \text{ rpm}}{60} = 5 \text{ rps} \]

### Step 2: Calculate the Angle Rotated in One Second
Now that we have the angular velocity in revolutions per second, we can find out how many revolutions the wheel makes in 1 second. Since the wheel rotates at 5 revolutions per second, it will complete 5 revolutions in 1 second.

### Step 3: Convert Revolutions to Radians
We know that one complete revolution is equal to \(2\pi\) radians. Therefore, to find the angle in radians for 5 revolutions, we multiply the number of revolutions by \(2\pi\):

\[ \text{Angle in radians} = 5 \text{ revolutions} \times 2\pi \text{ radians/revolution} = 10\pi \text{ radians} \]

### Conclusion
Thus, the angle through which the wheel rotates in 1 second is \(10\pi\) radians.

### Final Answer
The correct option is 3: \(10\pi\) radians.

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