Answer: Conversion of 9.83 m/s with a radius of 0.85 m into rotations per minute (rpm) is [tex]99.25 m^{-1}[/tex].
Explanation:
Given: Speed = 9.83 m/s
Convert m/s into m/minute as follows.
[tex]1 min = 60 sec\\9.83 m/s = 9.83 m/s \times \frac{60 s}{1 min}\\= 529.8 m/min[/tex]
Radius = 0.85 m
Now, rotations take place in circular motion. So, the circumference of a circle is [tex]2 \pi r[/tex].
Therefore, circumference is calculated as follows.
[tex]Circumference = 2 \times pi \times r\\= 2 \times 3.14 \times 0.85 m\\= 5.338 m[/tex]
Formula used to calculate rotations per minute (rpm) are as follows.
[tex]rpm = \frac{speed (in meter per minute)}{circumference}\\= \frac{529.8 m/min}{5.338 m}\\= 99.25 m^{-1}[/tex]
Thus, we can conclude that conversion of 9.83 m/s with a radius of 0.85 m into rotations per minute (rpm) is [tex]99.25 m^{-1}[/tex].
