Scientists submerge a paddle wheel in a stream and watch its rotational speed to determine the current's speed. If the paddle wheel has radius 0.20 m and rotates at 100 rpm, find the speed of the current in m/s.

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Jason Farmer

Answered question

2021-06-27

Scientists submerge a paddle wheel in a stream and watch its rotational speed to determine the current's speed. If the paddle wheel has radius 0.20 m and rotates at 100 rpm, find the speed of the current in m/s.

Answer & Explanation

okomgcae

Skilled2021-06-28Added 93 answers

As measured in radians per unit of time, the linear velocity v and the angular velocity w are related by: $v = r w$
where r is the radius.
First, we convert the angular velocity to rad/s:

$w = \frac{100 r e v}{m i n} \times \frac{2 π r a d}{1 r e v} \times \frac{1 m i n}{60 s} = (\frac{10 π}{3}) \frac{r a d}{s}$

Substitute $r = 0.20$ m and $w = (\frac{10 π}{3}) \frac{r a d}{s}$ :

$v = 0.20 (\frac{10 π}{3})$

$v \sim 2.1 m / s$

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