Question

To measure the speed of a current, scientists place a paddle wheel in the stream and observe the rate at which it rotates. If the paddle wheel has rad

Transformation properties
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asked 2021-06-27
To measure the speed of a current, scientists place a paddle wheel in the stream and observe the rate at which it rotates. If the paddle wheel has radius 0.20 m and rotates at 100 rpm, find the speed of the current in m/s.

Expert Answers (1)

2021-06-28

The linear velocity v and angular velocity w (in radians per unit time) are related by: \(v=rw\)
where r is the radius.
First, we convert the angular velocity to rad/s:

\(w=\frac{100rev}{min}\times\frac{2\pi rad}{1rev}\times\frac{1min}{60s}=(\frac{10\pi}{3})\frac{rad}{s}\)

Substitute \(r=0.20\) m and \(w=(\frac{10\pi}{3})\frac{rad}{s}\):

\(v=0.20(\frac{10\pi}{3})\)

\(v \sim 2.1 m/s\)

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