So we got this as homework today, and I just don't understand it; how to start or how to do it.
Explanations and/or setups would be great :)
A wheel with radius of $5$ feet is rotating at $100$ rpm.
a) Determine the angular speed of the wheel in radians per minute.
b) Determine the linear speed of a point on the circumference of the wheel in feet per minute.
Thank you so much.
This question is probably a better fit for Physics.SE. (Don't worry about that, though--if it is a better fit there, it will be moved without you having to do anything.)
EDIT: Spoiler Alert. I kinda forgot this was homework. I walk through solving the problems, so if you don't want to see it, don't look...
:)Anyway... The first part simply asks for you to find angular speed in radians per minute. This is a somewhat simple unit conversion, if you have learned about radians. Recall from trigonometry (and I guess precalc--not sure where they're introduced) that there are $2\pi$ radians in one revolution. That is, $2\pi \text{ rad} = 1\text{ rev}$.
Converting units:
$$\begin{array}{c|c} 100\text{ rev} & 2\pi \text{ rad} \\ \hline \text{min} & \text{rev} \end{array} = 200\pi\frac{\text{rad}}{\text{min}}\approx 628\frac{\text{rad}}{\text{min}}$$
Second part: This one is a little more tricky--that is, you need to know a physics formula: $$v=r\omega$$ This is one you should memorize and hold dear--it will serve you well throughout the rest of your studies of rotary motion. Now that I've said it's important, what does it mean? Well, this equation relates linear velocity and rotational velocity. $\omega$ represents rotational velocity in $\frac{\text{rad}}{\text{some time unit}}$, $r$ is the radius of the rotating body, and $v$ is linear velocity.
Using that equation, and the previous result: $$v=r\omega$$ $$v=(5\text{ feet})\left(628\frac{\text{rad}}{\text{min}}\right)\approx3141\frac{\text{feet}}{\text{min}}$$
Addendum: Because I worked that problem, I'll create a somewhat new one for you that uses similar concepts: