Question

Speed of a Current 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 a radius of 0.20m and rotates at 100rpm, find the speed of the current in m/s.

Short answer

2.09 min/sec.

Step-by-step solution

Step 1. Given information.

Convert the angular speed of rpm in rad/min., then use the formula$r=vw$ to find the linear speed in m/sec.
The given values are:
Radius $r=0.20m$, and angular speed $w=180rpm$.
To find:
Linear speed in m/sec.

Step 2. Finding the value of ω.

As we know that 1 revolution $=2\pi$radian

Thus, 100 revolution $=628$radian

Angular speed in rad/sec$\omega =\frac{628}{60}$

$\omega =10.466\text{rad}/\text{sec}$.

Step 3. Finding the linear speed.

The linear speed$v=rw$

$v=0.20\left(10.466\right)$

$v=2.09\text{m/sec}$

Thus, this is the value of linear speed in m/sec.