Now, let's look a little more carefully at the nature of these rotational vectors and which way they point. So first of all, they all point along the axis of rotation, all along the rotation axis. The angular displacement, the angular velocity, the angular acceleration, and later when we do the angular momentum and the torque, they all along the rotation axis. But there's one other part, for the direction along that axis, I'll call that the plus minus, right? Which way is positive? Which way does it point? We use the right hand rule, so right-hand rule is tricky. Later when you use it to do cross products will need to talk about it again. And when you use it in strange feels like electricity and magnetism where you can't picture things can be hard to use, but in rotational motion is probably the easiest place to use it. Because things are actually curving in your fingers actually curve, so will start out with. This is not a full discussion of the right-hand rule, just a few tips to get us started. So I like to give a few guidelines though, for the right-hand rule. Number 1 use, your right hand, I had undergraduates almost in tears and like I can't get the right-hand rule work, [SOUND] is because they're using their left hand. You gotta use your right-hand, that's why it's called right-hand rule. Two, curve your fingers naturally. Sometimes a lot of people trying to get their fingers to curve back, another your fingers curve like this, all right? So don't try to break your fingers the other way, all right? And three, as you do this, you make your fingers go with the rotating part. Your thumb is the vector. Okay, so we're going to apply this to the problem we just did, we have a wheel and it's rotating. And what we did is we kind of gave it a negative, a slowing, and angular deceleration and made it stop. So I want to think about all those vectors, so one of them are, well, the rotation axis I can illustrate with my Teflon rod. I'll turn this a little bit, but the rotation axis is here, so we're spinning around that rotation axis. So I already told you all the vectors are going to be along that axis. We just have to now think about which way they're going to point, right? So let me draw it a little bit of an angle here, so here is the wheel and here's the center, and here's the spokes. Sound like to draw spokes and it's kind of like that. It's got some thickness to it. There we go, there is wheel and it's spinning around. I'll say that this side is kind of going around like that and this side is going around like that. Whenever you draw those little arrows curved arrow that show motion, they're not vectors. You're just drawing those to help you see it, right? So the axis rotational course, is like this right through the center, like that spinning along that axis. So now, we just gotta come up with our displacement. Angular displacement, angular velocity, angular acceleration, vectors, right? They're all along this axis, so it's rotating this way, right? This part is going to the back. This back part is coming to the front. So the way to get the direction of the displacement between two little times is you make your fingers curl along with the rotation, right? If it's going out and in like this, take my right hand, make my fingers do that, the delta theta, the angular displacement between two points must be this way. It's going to be along the axis rotation, so this must be the delta theta vector, right? Because of the way it's curving. The omega vector, the angular velocity is always the same direction as delta, is this angular displacement, right? Because, omega is angular displacement over T, T is just a scalar, right? So if this is delta theta, this also must be omega, the direction of omega. And you can also get that with the right-hand rule if you just think about how it's rotating and you have your fingers go along with the rotation, with the angular velocity. Your thumb is out in that direction, but then we gotta think about alpha. So we have now, kind of defined this is the positive rotation direction, all right? So as theta increases in time, it's going to go in the positive direction. We just decided to positive direction, and we know that alpha came out negative, all right? So if our rotation tells us that this way is positive in alpha came out negative, it must have been this way. And it makes sense that alpha is in the opposite direction as omega, because it's slowing omega down, all right? So omega, the change in omega equals alpha times time. Well, if we take this thing times time and add it to this vector and this vector is going to get smaller, all right? So it makes sense that alpha's opposite direction with omega because it's a deceleration. But the positive direction was set by the motion, the motion said, positive rotation is this way. So that's how you work on those in problems. Right now, it's fairly straightforward when you get into torques and angle of minimum and procession, it gets more complicated, but let's start simple.
