Rate of Rotation for a Pulley (Question for a Reasoning/Thinking Skills Test)

AI Thread Summary
The discussion revolves around calculating the rate of rotation for multiple pulleys based on their diameters and the rate of rotation of the first pulley. The key formula mentioned is v = rω, where 'v' is linear velocity, 'r' is the radius, and 'ω' is the angular velocity. Participants share calculations showing how to derive the rates of rotation for pulleys B and C from the given data about pulley A. There is a request for a more intuitive understanding of the formula v = rω, especially for those with limited physics background. The conversation highlights the importance of understanding the relationship between pulley sizes and their rotation rates.
vertciel
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Homework Statement



*Please note that the following question is for a reasoning/thinking skills test. As I have only studied physics up to junior year in high school (and did not study pulleys then), I am unsure of the depth of physics knowledge required in this question, though it seems to involve some physics.

[PLAIN]http://img225.imageshack.us/img225/1577/imgsb.jpg


Homework Equations





The Attempt at a Solution



Since the rate of rotation for pulley A is given, it seems that I am to find the rate of rotation for pulley B, and then C using the diameters of the three pulleys. However, I am not familiar with the relationship between rate of rotation and diameters of pulleys.

Thank you very much for your help.

vertciel
 
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A vital equation would be v=rω where 'r' is the radius and 'ω' is the rate of rotation.
 
Thanks for your response, rock.freak667.

I have done some work, shown below, and have arrived at the correct answer. However, could someone please explain the formula v = rω ? How can I see this formula intuitively (especially since I have little background in physics)?

Thank you!

scherz0

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Given information \Rightarrow radius of Pulley A and smaller, inner pulley at B = \frac{1}{2} m, radius of outer pulley at B = 1 m, and radius of C = 2 m.

\Rightarrow Circumference of A and inner B pulley = \pi, Circumference of outer B = 2 \pi, Circumference of C = 4 \pi.

So A makes 8 turns/s \Rightarrow A makes \frac{1}{2}\frac{8 \pi}{s}= \frac{4 /pi}{s} \Rightarrow outer B makes \frac{4 \pi}{s} \div 1 \pi = \frac{4 \pi}{s} \Rightarrow inner B makes \frac{4 \pi}{s} /times 2 = \frac{8 \pi}{s} \Rightarrow C makes \frac{8 \pi}{s} \div 2 = \frac{4 \pi}{s} = Circumference of C \Rightarrow C makes 1 complete turn every second.
 
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vertciel said:
Thanks for your response, rock.freak667.

I have done some work, shown below, and have arrived at the correct answer. However, could someone please explain the formula v = rω ? How can I see this formula intuitively (especially since I have little background in physics)?


This http://hyperphysics.phy-astr.gsu.edu/hbase/rotq.html#avel" should help a bit.
 
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