How to Calculate Beta Angle for Pulley B in a Frictional Belt and Pulley System?

[masterflex]

Homework Statement

I've attached a picture of the problem. I couldn't get beta=120 degrees, for pulley B. How do you get that. Could the question be mistakenly missing this info in the question?

 

[masterflex]

I was thinking about it and drawing circles and lines. Can you tell me if this is a general rule (please look at attachment where I draw circles): when lines are drawn (simulating a rubber band around 2 pulleys), adding blue arcs from both circles will always equal 360 degrees? The blue arc from one circle, and the yellow arc from the other circle are equal in terms of the contact angle, yes?

 

[Double A]

They get beta = 120 from the given angle of 60 degrees.

180 - 60 = 120 degrees

The 60 degrees is referancing from the top of the pulley. To change the referance point to the bottom of the second pulley they performed the above calculation.

Also, since their referance point is perpendicular to the belt on both pullies they are parallel to each other so the angle referances can then be translated from the larger pulley to the smaller pulley.

 

[masterflex]

cool, thx.