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
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 $$w=(\frac{10\pi}{3})\frac{rad}{s}$$:

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

$$v \sim 2.1 m/s$$