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**masters** If an object moves along a circular path of radius **r** units, then its linear velocity, **v**, is given by:

$\displaystyle v=r\frac{\theta}{t}$

where $\displaystyle \frac{\theta}{t}$ represents the angular velocity in radians per unit of time.

480 revolutions = $\displaystyle 480 \cdot 2\pi$ radians per minute or $\displaystyle 960 \pi$ radians per minute.

$\displaystyle r=13in$

Here it is in one fell swoop:

$\displaystyle 13in \times \frac{1ft}{12in} \times \frac{1mi}{5280ft} \times \frac{480rev}{1min} \times \frac{2\pi}{1rev} \times \frac{60min}{1h}\approx37.13mph$

And here it is all broken out:

$\displaystyle v=13in \cdot \frac{440 \cdot 2\pi \ \ rad}{1 \ \ min}=39207.0763 \ \ in/min$

This translates to $\displaystyle 39207.0763 \times 60min = 2352424.579\ \ in/hr$.

$\displaystyle 1\ \ mi = 5280 \ \ ft = 63360 \ \ in$

$\displaystyle 2352424.579 \ \ in/hr \div 63360\ \ in/mile\approx 37.13\ \ mph$

Find the circumference of the wheel

$\displaystyle C = \pi D=26\pi in$

$\displaystyle \frac{80mi}{1hr}\times\frac{5280ft}{1mi}\times\fra c{12in}{1ft}\times\frac{1rev}{26\pi in}\times\frac{1hr}{60min}\approx1034.26$ rev/min

The miles, inches, feet, and hours cancel leaving you with revolutions over minutes