A wheel makes 180 revoluations in 1 minutes. Through how many radians does it turn in 1 second ?

Options

A. `(12pi)^(c )`
B. `(6pi)^(c )`
C. `(4pi)^(c )`
D. `(8pi)^(c )`

Answer

To find out how many radians a wheel turns in one second when it makes 180 revolutions in one minute, we can follow these steps:

### Step 1: Understand the relationship between revolutions and radians
One complete revolution of a wheel corresponds to an angle of \(2\pi\) radians.

### Step 2: Calculate the total radians for 180 revolutions
Since one revolution is \(2\pi\) radians, for 180 revolutions, the total angle in radians is:
\[ \text{Total radians} = 180 \times 2\pi = 360\pi \text{ radians} \]

### Step 3: Convert the time from minutes to seconds
The problem states that the wheel makes 180 revolutions in one minute. We need to convert this time into seconds. Since 1 minute is equal to 60 seconds, we have:
\[ \text{Time in seconds} = 60 \text{ seconds} \]

### Step 4: Calculate the radians turned in one second
To find out how many radians the wheel turns in one second, we divide the total radians by the total time in seconds:
\[ \text{Radians per second} = \frac{360\pi \text{ radians}}{60 \text{ seconds}} = 6\pi \text{ radians} \]

### Final Answer
Thus, the wheel turns \(6\pi\) radians in one second.

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