Angular and Linear Motion problem

AI Thread Summary
To find the angular velocity of a nail lodged in a car tire, the radius is 13 inches, and the car travels at 55 miles per hour. The circumference of the circle made by the nail is calculated, leading to the determination of how many revolutions occur in one hour. The relationship between linear speed and angular velocity is clarified, simplifying the problem. Ultimately, the solution confirms that calculating angular velocity can be straightforward when the correct relationships are applied.
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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.
 
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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.
 
yeah, it is 63360 into 1 mile. quite absurd but what can I do :(

The circumference I get is .001289163652 mi.
 
Move out of the US haha :-p

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?
 
If only it were that simple!

Thanks for your help, I have it understood now! :)
 
It IS that simple :wink: No problem, have a nice day.
 

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