What is the angular velocity of a cylinder in rev/hr

[karush]

An offset press cylinder has a $13.37\text {in}$ diameter.

The linear speed is $\displaystyle\frac{16.53 \text{ ft}}{\text{sec}}$

What is the angular velocity $(\omega)$ in $\displaystyle\frac{\text{rev}}{\text {hr}}$

from $v=r\omega$ then

$\displaystyle\frac{16.53\text{ ft}}{\text{sec}}
\cdot\frac{3600\text {sec}}{\text {hr}}
\cdot\frac{1}{6.685\text{ in}}
\cdot\frac{12\text { in}}{\text {ft}}
\approx\frac{106821\text{ rev}}{\text{hr}}$

this ans looks to large?

 

[MarkFL]

Re: what is the angular v of a cylinder in rev/hr

You answer is correct...it is spinning many times per second and there are many seconds per hour. :D

 

[karush]

Re: what is the angular v of a cylinder in rev/hr

well that cool...

I still don't know how to really deal with the words "rev" and "rad" in an equation?

 

[topsquark]

Re: what is the angular v of a cylinder in rev/hr

well that cool...

I still don't know how to really deal with the words "rev" and "rad" in an equation?

A rev(olution) is once around the circle. This corresponds to an angle of 2pi radians. Thus 1 rev = 2pi rad.

-Dan

 

[CellCoree]

I would first clarify the units being used. The linear speed given is in feet per second, while the diameter of the cylinder is given in inches. To calculate the angular velocity in revolutions per hour, we need to ensure that all units are consistent. Therefore, the linear speed needs to be converted to inches per hour.

Converting the linear speed of 16.53 feet per second to inches per hour, we get:

$\displaystyle\frac{16.53\text{ ft}}{\text{sec}}
\cdot\frac{3600\text {sec}}{\text {hr}}
\cdot\frac{12\text { in}}{\text {ft}}
= 712080\text{ in/hr}$

Now, using the formula $v=r\omega$, where $v$ is the linear speed, $r$ is the radius of the cylinder (half of the diameter), and $\omega$ is the angular velocity, we can solve for $\omega$.

$\omega=\displaystyle\frac{v}{r}=\frac{712080\text{ in/hr}}{6.685\text{ in}}\approx\frac{106627\text{ rev}}{\text{hr}}$

This is a more accurate answer for the angular velocity of the cylinder in revolutions per hour. It is important to always check and convert units to ensure consistency and accuracy in calculations.