Question

Find the exact rotation in revolutions per minute with the angular speed below:

Answer 1

The exact rotation in revolutions per minute is 1.125 revolutions per minute

`\omega = 1.125 \ (Revolution)/(minute)`

Explanation:

The given angular velocity is expressed as follows;

`\omega = 135 \cdot \pi \ (rad)/(h)`

Therefore, we have;

`\omega = (135 )/(60) \cdot \pi \ (rad)/(minute) = (9)/(4) \cdot \pi \ (rad)/(minute) = 2.25 \cdot \pi \ (rad)/(minute)`

One (1) revolution = 2·π radian

Therefore;

π radian = 1/2 revolution

2.25·π radian = 2.25 × 1/2 revolution = 1.125 revolution

Which gives;

`2.25 \cdot \pi \cdot (rad)/(minute) = 1.125 \ (Revolution)/(minute)`

The exact rotations in revolutions per minute is 1.125 revolutions per minute.