Question about angular speed??

Question

Okay, I have tried EVERYTHING, but I can't seem to get this! I don't know why! Maybe it's because I'm missing some part (i.e. the theta part) of my equation, but maybe someone can help me... I'll pick a best answer TODAY! Thank you SO much! Please show me step-by-step how to solve this! Thanks!

This text was printed on a four-color web heatset offset press. A cylinder on this press has a 13.37 inch diameter. The linear speed of a point on the cylinder's surface is 18.33 feet per second. What is the angular speed of the cylinder, in revolutions per hour?

What also confuses me is, should the units be in feet or inches? I've tried both, but I can't seem to get it! Hmmmmmm!

Answer 1

The relation between linear speed and angular speed is
Linear speed = Angular speed * Radius

If the linear speed is in feet per second and the radius is also in feet then the angular speed will be in radian per sec.

Here the linear speed and diameter are given. So we first find the angular speed.

The radius of the cylinder is 13.37/2 = 6.685 inch = 6.685/12=0.557083 feet, because 12 inches make a feet..

The linear speed is 18.33 feet per sec

So Angular speed = Linear speed/Radius
= 18.33/0.557083 = 32.90 radian per sec.

We know that a complete revolution is an angle of 2*PI radian

So 32.90 radian per sec = [32.90/(2*PI)] revolution per sec
Taking the value of PI as 3.14159, we get the angular speed as
32.90/(2*3.14159) = 5.2367 revolution per sec.

We know that in one hour there are 60*60=3600 seconds.

So 5.2367 revolution per sec = 5.2367*3600 =18852.3255 revolutions per hour.

Answer 2

13.37 inch dia circumference of 42.003058

[18.33 x 3600 ] /42.0030508 =1571 revolutions per hour

1571 x 360 = 565,557.33 degree per hour

3142 pi revolutions per hour

That press is rolling at 12 1/2 miles an hour