angular/linear speed

[intervade]

Ok, I have a couple of different problems that I'm having a hard time understanding how to setup. They are both similar.

The first:
The diameter of each wheel of a bicycle is 26inches. If you are traveling at a speed of 35 miles per hour on. How many revolutions per minute are the wheels turning?

I know I have a radius of r = 13 and the speed is 35 miles per hour. I was given a previous problem that gave me the revolutions per (second) and I needed to solve for miles per hour, but I'm still having a hard time setting this up.

The Second problem: (Linear speed on earth)
Earth rotates on an axis through its poles. The distance from the axis to a location on earth 30 degrees north latitude is about 3429.5 miles. Therefore a location on earth at 30 degree north latitude is spinning on a circle of a radius 3429.5. Compute the linear speed on the surface of earth at 30 degree north latitude. This one just confuses me. Do I assume that I have a angle of 30 degrees? Therefor 30 * pi/180 .... 6pi radian?

Am I looking at both of these wrong?

 

[galactus]

The first:
The diameter of each wheel of a bicycle is 26inches. If you are traveling at a speed of 35 miles per hour on. How many revolutions per minute are the wheels turning?

The circumference of the wheel is \(\displaystyle 2{\pi}\cdot 13=26{\pi} \;\ inches\)

\(\displaystyle \frac{26\pi}{12}=\frac{13\pi}{6}=6.8068 \;\ \text{feet per revolution}\)

\(\displaystyle \frac{5280}{\frac{13\pi}{6}}=775.7 \;\ \text{revolutions per mile}\)

\(\displaystyle 35\cdot(775.7)=27,149.5 \;\ \text{revolutions per hour}\)

\(\displaystyle \frac{27,149.5}{60}=452.5 \;\ \text{revolutions per minute}\)