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 .
Part:
Part 2 of 3
(b) Find the speed of the current in . Round to one decimal place.
The speed of the current is approximately
.

Ask by Herrera Peterson. in the United States

Mar 23,2025

Question

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 .
Part:
Part 2 of 3
(b) Find the speed of the current in . Round to one decimal place.
The speed of the current is approximately
.

Ask by Herrera Peterson. in the United States

Mar 23,2025

UpStudy AI · Accepted Answer

1. The angular speed is given as $$\omega = 15$$ rpm. We first convert this to radians per minute:
   $$
   \omega = 15 \times 2\pi \approx 15 \times 6.2832 \approx 94.2 \; \mathrm{rad/min}
   $$

2. The linear speed at the rim of the wheel, which equals the speed of the current, is computed by:
   $$
   v = r \omega
   $$
   where $$r = 4 \, \mathrm{ft}$$ and $$\omega \approx 94.2 \, \mathrm{rad/min}$$. Thus,
   $$
   v \approx 4 \times 94.2 = 376.8 \, \mathrm{ft/min}
   $$

The speed of the current is approximately $$376.8 \, \mathrm{ft/min}$$.
The angular speed is approximately $$94.2 \, \mathrm{rad/min}$$. The speed of the current is approximately $$376.8 \, \mathrm{ft/min}$$.

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