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

[vertciel]

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

 

[rock.freak667]

A vital equation would be v=rω where 'r' is the radius and 'ω' is the rate of rotation.

 

[vertciel]

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.

 

[rock.freak667]

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.