A wheel make 450 revolutions per hour. The number of radians through which its turn in one second is

Options

A. `pi/4`
B. `pi/2`
C. `pi/6`
D. `pi/3`

Answer

To find the number of radians through which a wheel turns in one second, we can follow these steps:

### Step 1: Convert revolutions per hour to revolutions per second
Given that the wheel makes 450 revolutions per hour, we need to convert this to revolutions per second.

1 hour = 3600 seconds, so:
\[ \text{Revolutions per second} = \frac{450 \text{ revolutions}}{3600 \text{ seconds}} = \frac{450}{3600} = \frac{1}{8} \text{ revolutions per second} \]

### Step 2: Convert revolutions to radians
We know that 1 revolution is equal to \(2\pi\) radians. Therefore, to find the number of radians per second, we multiply the number of revolutions per second by \(2\pi\):
\[ \text{Radians per second} = \left(\frac{1}{8} \text{ revolutions per second}\right) \times (2\pi \text{ radians/revolution}) = \frac{2\pi}{8} = \frac{\pi}{4} \text{ radians per second} \]

### Conclusion
Thus, the number of radians through which the wheel turns in one second is \(\frac{\pi}{4}\).

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