# How fast is the edge of the yo-yo spinning in mph

Tags:
1. Apr 9, 2017

### Vital

1. The problem statement, all variables and given/known data
Hello!
I am trying to solve the exercise, but I don't see my mistakes - I can't come up with a correct answer.
The exercise from the begging of trigonometry, so it has to be solved using concepts of a speed and angular velocity.

A yo-yo which is 2.25 inches in diameter spins at a rate of 4500 revolutions per minute. How

fast is the edge of the yo-yo spinning in miles per hour? Round your answer to two decimal

places.

2. Relevant equations
Here is how I am trying to solve it:
v = r x w,
where v is the speed, r radius, w is the average angular velocity, which equals to

w = 2π x f, where f is the frequency of revolutions and equals to number of revolutions / time

3. The attempt at a solution
Putting it all together I get:

r = 2.250 / 2 = 1.225
number of revolutions in one hour 4500 х 60 = 270 000
w = 2π × 270 000 = 1 695 600
v = 1.225 x 1 695 600 = 2 077 110 inches in one hour

Convert to miles:
2 077 110 / 63 360 = 32.78 miles per hour

But it should be 30.12 miles per hour.

Please, help me to find my mistake.
Thank you!

2. Apr 9, 2017

### BvU

Hello Vital,

It is always a good idea to estimate answers before typing them in on a calculator
But in this case it may have been a simple oversight ?
No it is not.

3. Apr 9, 2017

### Vital

Oh! Yes. It is a typo, which has gone through all calculations. And I actually do this type of calculations manually (some in mind, and others, with bigger numbers, on paper).
Thank you very much. Indeed an awkward situation. :)

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted