Question

What is the speed of a 3 cm diameter roll if it has a velocity of 1220 yards/hour?

Answer 1

Answer:

The speed of the roll is 1239.52 revolutions per minut (1239.52 rpm).

Step-by-step explanation:

In this problem we want to know the angular speed of the roll, knowing its tangencial speed (1220 yards/hour).

The relation between the angular speed and the tangencial speed is

$v=\omega*r=\omega*(D/2)$

$\omega=2v/D$

In this case we have a diameter of 3 cm and a velocity of 1220 yards/hour. So we can write

$\omega=2v/D=2*1220\frac{yards}{hour} *\frac{1}{3\,cm} *\frac{91.44cm}{1 yard} *\frac{1hour}{60min}= 1239.52 \frac{1}{min}=1239.52 rpm$

So the speed of the roll is 1239.52 revolutions per minut (1239.52 rpm).