To find out how many radians the wheel turns in one second, follow these steps:
1. Determine the number of revolutions per second:
- The wheel makes 270 revolutions in one minute.
- There are 60 seconds in a minute.
- To find the number of revolutions per second, divide the total revolutions per minute by the number of seconds in a minute:
[tex]\[
\text{Revolutions per second} = \frac{270 \text{ revolutions}}{60 \text{ seconds}} = 4.5 \text{ revolutions per second}
\][/tex]
2. Convert revolutions to radians:
- One revolution is equal to [tex]\(2\pi\)[/tex] radians.
- So the number of radians in one revolution is [tex]\(2\pi \approx 6.283185307179586\)[/tex] radians.
3. Calculate the total radians per second:
- Multiply the number of revolutions per second by the number of radians per revolution:
[tex]\[
\text{Radians per second} = 4.5 \text{ revolutions per second} \times 6.283185307179586 \text{ radians per revolution}
\][/tex]
[tex]\[
\text{Radians per second} \approx 28.274333882308138 \text{ radians per second}
\][/tex]
Therefore, the wheel turns approximately [tex]\( 28.274 \)[/tex] radians in one second.
