So my professor gave us a bunch of problems to review over the weekend and I was able to do most of them with no problem. However this problem really confuses me. It's not being graded, but I would love if someone can help me set the problem up into an equation and walk me through it. I just want to learn and understand it more clearly. Thank you very much I truly appreciate it! I'm not very good at the script formatting on this site so I'll include a picture of the problem and a picture of me trying to do it on my notebook.
In an automobile transmission a gear ratio g is the ratio : $g= \frac{\text{angular speed of engine} }{\text{angular speed of wheels}} $
The angular speed of the engine is shown on the tachometer (in rpm). A certain sports car has wheels with radius 11 in. Its gear ratios are shown in the following table. Suppose the car is in fourth gear and the tachometer reads 3500rpm.
1st gear = ratio 4.1
2nd gear = ratio 3.0
3rd gear = ratio 1.6
4th gear = ratio 0.9
5th gear = ratio 0.7
a) find the angular speed of the engine.
b) find the angular speed of the wheels
c) How fast (in mph) is the car traveling?
It looks like you are starting out right at least, but I can't read what's written on your paper very easily. Anyway, as you noted, since the car in in $4$th gear, the gear ratio is $.9,$ and we are told that the angular speed of the engine is 3500 rpm. Therefore, the angular speed of the wheels is $$\frac{3500}{.9}=3888.889\text{ rpm }$$ The radius of the wheel is $11$ inches so in one revolution it rolls $22\pi$ inches, and in one minute it travels $3888.889\cdot 22\pi$ inches.
Now you just have to convert inches per minute into miles per hour.