Expert: Paul Klarreich - 2/1/2007

Question
The figure is a side view of 3 rollers that are tangent to one another.

If roller A turns at 120 revolutions per minute, at what angular velovities do rollers B and C turn?

i drew out the figure for you.
http://img01.picoodle.com/img/img01/7/1/31/f_precalci_bc51m_a53001a.png

thanks in advance!

Answer
Questioner:  Jennie
 
Question:  
The figure is a side view of 3 rollers that are tangent to one another.

If roller A turns at 120 revolutions per minute, at what angular velocities do rollers B and C turn?

I drew out the figure for you.
http://img01.picoodle.com/img/img01/7/1/31/f_precalci_bc51m_a53001a.png

thanks in advance!
..........................
Hi, Jennie,

OK, I found it.  The principle to apply here is that the linear velocities of the circumferences of the rollers are all the same.  Then, writing:

V = the linear velocity at the circumference.
Omega = the angular velocity of a roller.
r = radius of a roller.

We have   V = r Omega, where Omega is in radians/second.

Since all the V's are constant, that means:

rA OmegaA = rB OmegaB = rC OmegaC

rA = 3
rB = 2
rC = 4.8
OmegaA = 120*2pi

rA OmegaA = 720pi.

Now rB OmegaB = 720pi
2 OmegaB = 720pi
OmegaB = 360pi, or 180 revs/sec.

Now rC OmegaC = 720pi
4.8 OmegaC = 720pi
OmegaC = 720pi/4.8 = 7200pi/48 = 600pi/4 = 150pi = 75 revs/sec.