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

[Vital]

Homework Statement

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.

Homework 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

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!

 

[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 ?

r = 2.250 / 2 = 1.225

No it is not.

 

[Vital]

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.

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. :)

 

[StenliSuryadinata]

Hello Vital,

Some typo error could be quite annoying, it would be good for others if we could make some corrections to your solution.
I made some definition to some numbers in the question as to make simple.

v = r * ω
v = r * θ/t
v = linear velocity
r = radius
t = time

ω = 4500 revolution per minute
1 minute = 1/60 hour
ω = θ / t
ω = angular velocity

ω = 4500 * 2π radians / 1/60 hour = 540,000 π radians/hour
ω = 540,000 * 3.14 = 1,695,600

d = 2.25 inches
r = d/2 = 2.25/2 = 1.125 inches
63360 inches = 1 mile

r = 1.125/ 63360 miles

linear velocity = r * ω = 1.125/63360 * 1695600 = 1.125 * 26.764 = 30.12

Thank you