Angular and Linear Motion problem

[stf]

Homework Statement

Automobile Tire: If a car runs over a nail at 55 mi/hr and the nail is lodged in the tire tread 13 in. from the center of the wheel, then what is the angular velocity of the nail in radians per hour?

Homework Equations

w = alpha/time

a = s / r

The Attempt at a Solution

I am not really sure where to start on this, obviously 13 in. is the radius, but I am unsure of how to get the angle alpha without a sector length. I assume it has something to do with the given 55 mph but don't see where it goes in.

 

[Mentallic]

If it is lodged 13 inches from the centre of the tyre, then what is the circumference of the circle it makes around it?


p.s. there's no way I'm going to help with the units of that flawed imperial system.
x inches = 1 mile, where x is some crazy and unnecessarily complicated number.

 

[stf]

yeah, it is 63360 into 1 mile. quite absurd but what can I do :(

The circumference I get is .001289163652 mi.

 

[Mentallic]

Move out of the US haha

Ok so if the car is moving at 55mi/h and the circumference of the nail is ... that many miles, then how many revolutions will be made in an hour?

 

[stf]

If only it were that simple!

Thanks for your help, I have it understood now! :)

 

[Mentallic]

It IS that simple No problem, have a nice day.