Express the angular speed in radians per second.
-To approximate the speed of a river, a circular paddle wheel with radius $0.48$ feet is lowered into the water. If the current causes the wheel to rotate at a speed of 13 revolutions per minute, what is the speed of the current? Express the answer in miles per hour rounded to two decimal places, if necessary.
A) $0.45$ miles per hour
B) $0.07$ miles per hour
C) $39.21$ miles per hour
D) $0.22$ miles per hour

Question

Quizplus · Accepted Answer

The correct answer is A because:The speed of the current is equal to the circumference of the paddle wheel times the angular speed. The circumference of the paddle wheel is $2\pi r = 2\pi (0.48) = 3.02$ feet. The angular speed is $13 \text{ revolutions per minute} = 13 \times 2\pi \text{ radians per minute} = 81.68 \text{ radians per minute}$. Therefore, the speed of the current is $3.02 \text{ feet per minute} \times 81.68 \text{ radians per minute} = 246.5 \text{ feet per minute}$. Converting to miles per hour, we get $246.5 \text{ feet per minute} \times \frac{60 \text{ minutes}}{1 \text{ hour}} \times \frac{1 \text{ mile}}{5280 \text{ feet}} = 0.45 \text{ miles per hour}$.

Express the Angular Speed in Radians Per Second 0.480.480.48 Feet Is Lowered into the Water

Express the Angular Speed in Radians Per Second $0.48$ Feet Is Lowered into the Water