A circular paddle wheel of radius 4 ft is lowered into a flowing river. The current causes the wheel to rotate at a speed of 15 rpm,
Part 1 of 3
(a) What is the angular speed? Round to one decimal place.
The angular speed is approximately .

Did you know that the concept of angular speed has been around since the time of the ancient Greeks? Archimedes, in particular, studied levers and pulleys, setting the stage for our understanding of rotational motion. The beautiful mathematics behind angular speed can be traced back to this era, where the rotational aspects of circles and their relationships to linear motion began to take shape!

For a real-world twist, think about how paddle wheels have been instrumental in various modes of transportation, especially in boats and hydro power systems. The rotation generated by the river’s current isn’t just a source of mechanical advantage; it’s a practical application of converting potential energy in flowing water into kinetic energy. This principle underpins everything from steamboats to modern hydroelectric power!