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.

 

[rwisz]

,

I would approach this question by first identifying the key variables involved: the rate of rotation, the diameters of the pulleys, and the relationship between them. From my understanding, the rate of rotation for a pulley is directly proportional to its diameter. This means that as the diameter of a pulley increases, its rate of rotation also increases.

To solve this problem, I would use the formula for rotational speed, which is equal to the angular velocity divided by the circumference of the pulley. In this case, we are given the rate of rotation for pulley A, which is 60 revolutions per minute. We are also given the diameter of pulley A, which is 8 inches.

To find the rate of rotation for pulley B, we can use the formula:

Rate of rotation for pulley B = (Rate of rotation for pulley A) x (Diameter of pulley A / Diameter of pulley B)

Substituting the values given in the question, we get:

Rate of rotation for pulley B = (60 revolutions per minute) x (8 inches / 4 inches) = 120 revolutions per minute

Similarly, to find the rate of rotation for pulley C, we can use the formula:

Rate of rotation for pulley C = (Rate of rotation for pulley B) x (Diameter of pulley B / Diameter of pulley C)

Substituting the values given in the question, we get:

Rate of rotation for pulley C = (120 revolutions per minute) x (4 inches / 2 inches) = 240 revolutions per minute

Therefore, the rate of rotation for pulley C is 240 revolutions per minute.

In conclusion, the key to solving this problem is understanding the relationship between rate of rotation and diameter for pulleys. By using the appropriate formula and substituting the given values, we can easily find the rate of rotation for pulley B and C. I hope this helps and good luck on your reasoning/thinking skills test!