To find out how long the fly takes to move through an angular displacement of 2.1 radians given its average angular speed of 7.9 rad/s, we can use the formula for angular speed:
[tex]\[ \text{angular speed} = \frac{\text{angular displacement}}{\text{time}} \][/tex]
Rearranging this formula to solve for time, we get:
[tex]\[ \text{time} = \frac{\text{angular displacement}}{\text{angular speed}} \][/tex]
Given:
- Angular speed ([tex]\(\omega\)[/tex]) = 7.9 rad/s
- Angular displacement ([tex]\(\theta\)[/tex]) = 2.1 rad
We substitute these values into the equation:
[tex]\[ \text{time} = \frac{2.1 \, \text{rad}}{7.9 \, \text{rad/s}} \][/tex]
Calculating this gives:
[tex]\[ \text{time} \approx 0.266 \, \text{s} \][/tex]
Thus, the fly takes approximately 0.266 seconds to move through 2.1 radians.
