Answer:
The linear velocity of the conveyor belt is v=0.25 m/s.
Explanation:
In a circular motion, the tangential velocity can be written as
\(v_{t}=r\omega\)
where r is the radius of the circle, and ω is the angular velocity.
In this case, we were given some data: the radius r=0.5 meters, and the revolutions per minute of the rollers. The first thing we have to do is to calculate ω with the proper units, which is rad/second, using the given revolutions per minute, so
\(\omega=30\frac{rev}{min}*\frac{2\pi rad}{1rev}*\frac{1 min}{60 s}=\pi \frac{rad}{s}\)
because in 1 minute, there are 60 seconds, and in 1 revolution, there are 2π rad.
Now, we can calculate the answer:
\(v_{t}=r\omega=\frac{1}{2}m*\pi \frac{rad}{s}=\frac{1}{2}m*\frac{1}{2}\frac{1}{s}=\frac{1}{4}\frac{m}{s}\)
in which we had to convert rad/s to Hz (or 1/s), knowing that 2πrad=1Hz.
Therefore, the answer is v=0.25 m/s.
