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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:
Part 1 of 3
(a) What is the angular speed? Round to one decimal place.
The angular speed is approximately
.

Ask by Elliott Hamilton. in the United States
Mar 23,2025

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The angular speed is approximately .

Solución

Given that the paddle wheel rotates at 15 revolutions per minute (rpm), we first convert the revolutions to radians. Recall that one revolution is equal to radians.
  1. Express the angular speed in terms of radians per minute:
  2. Approximating using :
Thus, the angular speed is approximately .

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To find the angular speed in radians per minute, we need to convert the rotational speed from revolutions per minute (rpm) to radians per minute. Since one revolution is equivalent to radians, we can use the formula:
Substituting the values:
Rounding to one decimal place, the angular speed is approximately .

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