if an airplane propeller is rotating at 500 revolutions per minute. How do i find the linear speed at the tip of a propeller that is 3 meters long from tip to tip?
We assume the propeller shaft is in the middle! So the diameter of the propeller is $3$. Thus in one full revolution the tip travels through the full circumference $3\pi$. (Circumference is $2\pi r$, so $\pi d$.)
Thus in $1$ minute the tip travels a distance of $(500)(3\pi)$. If you want the speed in something other than metres per minute, you will have to make a conversion. For example, for kilometres per hour, multiply $(500)(3\pi)$ by $60$, then divide by $1000$. By the way, in km/hour, it is $\approx 282.743$. Fast!