Given
d: diameter
d = 41 cm
We need radius information so we will calculate it:
r: radius
r = d/2
r = 41/2
r = 20.5 cm
Rotating speed
w = 242 rpm
Procedure
At a distance r from the center of the rotation, a point on the object has a linear speed equal to the angular speed multiplied by the distance r. The units of linear speed are meters per second, m/s.
But before using the formula we need to have all the units in the same system. So we need to go from rpm to rad/s and from cm to m
![\begin{gathered} 242\cdot\frac{\text{rev}}{\min}\cdot\frac{2\text{ pi rad }}{1\text{ rev}}\cdot\frac{1\text{ min}}{60\text{ s}} \\ 25.34\text{ rad/s} \\ \\ 20.5\text{ cm}\cdot\frac{1m}{100\operatorname{cm}} \\ 0.205\text{ m} \end{gathered}]()
Now we can calculate the linear velocity of the belt.
Answer
The linear velocity of the belt would be 5.2 m/s.