To determine the angular speed of the second hand of a clock, follow these steps:
1. Understand the problem: We need to find the angular speed of a second hand. Angular speed is the rate at which an object rotates or revolves relative to another point, i.e., how many radians it sweeps per second.
2. Know the rotations and time:
- The second hand completes one full rotation in 60 seconds.
- One full rotation is equivalent to [tex]\(2\pi\)[/tex] radians.
3. Calculate angular speed:
- Angular speed ([tex]\(\omega\)[/tex]) is calculated using the formula:
[tex]\[
\omega = \frac{\text{total angle}}{\text{time}}
\][/tex]
- Here, the total angle for one full rotation is [tex]\(2\pi\)[/tex] radians and the time taken for that rotation is 60 seconds.
4. Insert the values into the formula:
[tex]\[
\omega = \frac{2\pi \text{ radians}}{60 \text{ seconds}}
\][/tex]
5. Simplify the expression:
[tex]\[
\omega = \frac{2\pi}{60}
\][/tex]
[tex]\[
\omega = \frac{\pi}{30}
\][/tex]
6. Approximation:
- Use a calculator to get the numeric value of [tex]\(\frac{\pi}{30}\)[/tex].
- [tex]\(\pi\)[/tex] is approximately 3.14159.
- So, [tex]\(\frac{3.14159}{30} \approx 0.1047\)[/tex].
7. Rounding to two decimal places:
- The value 0.1047 rounded to two decimal places is 0.10.
Therefore, the angular speed of the second hand is approximately [tex]\( \boxed{0.10} \)[/tex] radians per second.
