# To an order of magnitude, through how many revolutions will it turn?

• chocolatelover
In summary, an automobile tire is rated to last for 35,000 miles but will turn through 2*pi*r revolutions. To an order of magnitude, through how many revolutions will it turn? 1960788.899.
chocolatelover
Hi everyone,

## Homework Statement

An automobile tire is rated to last for 35,000 miles. To an order of magnitude, through how many revolutions will it turn?

2pir

## The Attempt at a Solution

d=3f=.9144m

r=.9144/2
=.4572

n(2pi)r=35,000miles

(35,000miles)=56327040meters

n(2pi)(.4572meters)=56327040meters

409867.3=
409868

Does that look right?

Thank you very much

I agree very much that you will need to do:

35,000 miles = (2*pi*r)n

n*2pi*.4572 = 56327040m
n = 409868 ? appears wrong, simply from putting those numbers into the calculator.

chocolatelover said:
An automobile tire is rated to last for 35,000 miles. To an order of magnitude, through how many revolutions will it turn?
...
409867.3=
409868

Does that look right?
No. First, you did something wrong. Second, your incorrect answer has too many digits. The question asks for the answer to an order of magnitude.

Work out the answer correctly to however many digits you want. After that, I will (or someone else) will show you how to calculate it to do these order of magnitude calculations.

Last edited:
Thank you very much

n*2pi*.4572 = 56327040m
n(2.872672322)=56327040m
n=1960788.899

Does that look right?

Could someone please show me how to convert it to the order of magintude?

Would that just be 1.96 X 10^6

The term order of magnitude means 1, 10, 100, etc. In other words, less than one significant digit. You are still using three significant digits.

Now that you have the correct numerical answer, here is an easy way to compute a rough estimate of the answer

$$N=\frac{l}{\pi d} = \frac{35000\,\text{miles}}{3\pi\,\text{feet}}$$

The first thing to recognize is that $3\pi$ feet is about 10 feet. After converting 35,000 miles to feet all we have to do is divide by 10. Multiplying 35,000 by 5,280 is a pain in the rear. Multiplying 30,000 by 6,000 is a lot easier, and will be close to correct:

$$(3*10^4)*(6*10^3) = 18*10^7 \approx 2*10^8$$

Dividing by 10 gives 20 million, which is correct to within an order of magnitude. (Actually, its even better than that; this is correct to one decimal place.)

Thank you very much

Regards

## 1. What does "to an order of magnitude" mean in this context?

"To an order of magnitude" refers to the power of 10 that a quantity is closest to. For example, if a quantity is 10^3 or 1000, it is said to be within one order of magnitude of 10.

## 2. How do you calculate the number of revolutions in this scenario?

The number of revolutions can be calculated by dividing the total distance traveled by the circumference of the object being rotated. This will give you the number of full revolutions. If there is any remaining distance, it can be divided by the circumference to calculate the number of partial revolutions.

## 3. What factors can affect the accuracy of this calculation?

The accuracy of this calculation can be affected by factors such as the precision of the measurements, the shape and size of the object being rotated, and any external forces acting on the object.

## 4. Is "order of magnitude" the same as "significant figures"?

No, "order of magnitude" refers to the size or scale of a quantity, while "significant figures" refer to the precision or certainty of a measurement. They are not interchangeable terms.

## 5. Can this calculation be applied to any type of motion or rotation?

Yes, this calculation can be applied to any type of motion or rotation, as long as the distance traveled and the circumference of the object are known.

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