Number of Revolution

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mathdad

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How many revolutions will a circular disk with a diameter of 4 feet have completed after it has rolled 20 feet?

What is the equation set up here?
 
How many revolutions will the disk have made when it rolls a distance equal to the circumference of the disk (assuming no slippage)?
 
How many revolutions will the disk have made when it rolls a distance equal to the circumference of the disk (assuming no slippage)?

The distance rolled in a single revolution is the circumference of the disk. This is pi(d), where d is the diameter. So, in this case that is 4pi.

To get the number of revolutions, I divide 20 by 4pi. Let R = number of revolution.

R = 20/4pi

R = 5/pi

Correct?
 
Let's check your answer using the arc-length formula:

[MATH]\theta=\frac{s}{r}=\frac{20\text{ ft}}{2\text{ ft}}=10\cdot\frac{1\text{ rev}}{2\pi}=\frac{5}{\pi}\text{rev}\quad\checkmark[/MATH]
 
Let's check your answer using the arc-length formula:

[MATH]\theta=\frac{s}{r}=\frac{20\text{ ft}}{2\text{ ft}}=10\cdot\frac{1\text{ rev}}{2\pi}=\frac{5}{\pi}\text{rev}\quad\checkmark[/MATH]

Another one for the files.
 
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