Question

Convert 9.83 m/s with a radius of 0.85 m to rotations per minute (rpm)

Answer 1

Answer: Conversion of 9.83 m/s with a radius of 0.85 m into rotations per minute (rpm) is $99.25 m^{-1}$.

Explanation:

Given: Speed = 9.83 m/s

Convert m/s into m/minute as follows.

$1 min = 60 sec\\9.83 m/s = 9.83 m/s \times \frac{60 s}{1 min}\\= 529.8 m/min$

Radius = 0.85 m

Now, rotations take place in circular motion. So, the circumference of a circle is $2 \pi r$.

Therefore, circumference is calculated as follows.

$Circumference = 2 \times pi \times r\\= 2 \times 3.14 \times 0.85 m\\= 5.338 m$

Formula used to calculate rotations per minute (rpm) are as follows.

$rpm = \frac{speed (in meter per minute)}{circumference}\\= \frac{529.8 m/min}{5.338 m}\\= 99.25 m^{-1}$

Thus, we can conclude that conversion of 9.83 m/s with a radius of 0.85 m into rotations per minute (rpm) is $99.25 m^{-1}$.