Hey, guys. So now that you've solved a bunch of rotation questions using energy and a whole bunch of other questions using torque, you might have noticed that some of these questions are very similar. For example, we did yo-yo equations for both energy and torque. Now what I want to do in this video, which is really, really critical, is to do an overview of these two methods so you know which one to use in different situations. Let's check it out.
So I want to remind you real quick that in some linear motion problems, we could solve them using either f=ma and motion equations. Remember, we have those 3 to 4 motion equations, kinematics equations. So we could use a combination of these two methods to solve them. I'm going to call this, method 1. Or we could have used the conservation of energy equation, method 2. We typically, most people learn method 1 first, and then they learn method 2. Number 2 is usually better because you have one equation instead of having two equations, and instead of having to worry about which out of the 3 to 4 motion equations to pick from. Alright?
So I want to show you this in linear motion and then we're going to bring it back to rotation, real quick. Right? So if you have a block here, and the block slides on an incline, and let's assume it's frictionless, there are two ways you can find the velocity at the bottom. If you want to find v final at the bottom here, there are two ways. The first way I'm going to use is f=ma and equations, so motion equations. What you would do, just like any motion problem, is to list your variables: the initial, the final, a delta x, delta t. Let's say it starts from rest. So v initial 0 , v final is what we're looking for. Acceleration, we don't have. Delta x and delta t. Let's say we have the initial height. So, and the angle. Let's say these are given. So from these, you would be able to find your delta x. Right? Because h=Δx∘sin(θ). So if I give you these two, you can find this one. You would have some delta x as well. You wouldn't have delta theta. That would be your ignored variable. But notice that to solve this, you need to know two things. So you would know v initial . You could find delta x. You would be missing acceleration. So what you would do to find acceleration is write sum of all forces equals ma. And in this case, the only force that matters here is mgx. You have mgx pulling this thing down the plane. Mgy will cancel with normal, and there are no other forces. So when I write sum of all forces in the x-axis, I have mgx equals max. Mgx is mgsin(θ) and equals ma. We're just going to call it a. The masses cancel, and I'm left with an acceleration. So at this point, I know the acceleration. I can plug it in here. I know the acceleration. I can plug it in there. And I can use the fact that my ignored variable is delta t to know that I have to use the second equation, which is v final 2 = v initial 2 +2aΔx. It's the only equation that doesn't have delta t. So I can solve here. I can cancel this out.
This is much better to do using energy. To do this using energy, we're just going to use the conservation of energy equation: K initial + U initial +work non-conservative= K final + U final . K initial is 0 because it starts from rest. I have some height in the beginning. So this is mghinitial. Work non-conservatives is the work done by you. You're not doing anything; you're just watching, plus the work done by friction. There is no friction, so this is 0. At the end, we have kinetic energy because we have linear motion. So this is 12m v final 2 , and there is no potential energy at the end because you're at the lowest points. Cancel the masses, and v final is 2ghinitial. This height here is obviously the initial. I end up at the same place. So given the choice of methods, you would obviously choose the energy way of solving things because it is better. Now it's better for velocity. If you're looking for acceleration, you would have to use f=ma to find acceleration.
Similar to how there are two ways to solve problems, we're going to have the same thing in rotational motion. Some problems, instead of being solved in rotation, will be solved with f=ma in motion equations, will be solved with torque=Iα in motion equations. And we're also going to have problems that we're going to be able to solve using conservation of energy. If you have the choice, which most of the time, unfortunately, you don't, you're going to want to pick this one, right? Because it's easier. But it really depends on what you're being asked or what you're being given, actually on what you're being given. Right? So generally, you will use torque=Iα if you're either being asked or given a or alpha. So if I ask for a, you're going to use it, or if I give you a and ask for something else, you're going to use torque=I ‚. Conservation of energy is better for problems that are asking or giving velocity v or velocity, omega. You're always going to use motion equations if you're looking for time, time delta t, or if you need time to solve the problem somehow.
So I think this is really, really important to remember, and it helps a lot to make a combination of all these topics easier to work through. Sometimes, however, you're not going to have a choice. You'll be asked to do this in a specific way, even if you could have used an easier method. Sometimes a question will say, you know, using Newton's laws, which means f=ma, do this. So what professors will do sometimes is force a method upon you to make sure that you can't use an easier method.
So I want to do a quick example here of how questions may look almost identical but require different methods to solve. So a yo-yo spins around itself as it falls, something like this. The yo-yo is falling and spinning at the same time. So it has an a and a v, then it has an alpha and omega.
Find its acceleration after dropping 2 meters. We cannot use conservation of energy to find acceleration. If you look at the conservation of energy equation, there's no a in there. So we would have to use to find acceleration, a combination of f=ma, torque=Iα. The fact that it drops 2 meters doesn't matter. The acceleration is constant throughout. This is just extra information. Here, a yo-yo falls and, by the way, the reason you use both of these is because a yo-yo has linear acceleration and angular acceleration at the same time.
Now here, we want to know the speed after dropping 2 meters. Both pieces of information are important, and we're going to use energy. And then here, we want to know how long does it take to drop 2 meters. Drop 2 meters is delta y. And how long does it take is delta t. Because I'm being asked for time, you have to use motion equations. But it's very likely that motion equations are not going to be enough because to do this, you're going to have to have you're going to have to have acceleration. Let me list my five motion variables. Let's say you're dropping from rest. You don't know the final velocity, you don't know the acceleration. You're given delta y and you're looking for delta t. So you're going to have to either find the final using energy, or you're going to use f=ma and torque=Iα to find acceleration so that you can use motion equations. So here, to solve this, you're going to use motion plus and either f=ma or energy. Depending on which way you want to go.
Anyway, I hope this makes sense. Now that we've seen these two things, you might get some questions where you sort of need to know both. And I wanted to make this a little bit simpler. You might have noticed these questions are very similar, but they do require different methods. So I think this is crucial for you to master. I hope it makes sense. And if you have any questions, please let me know because I want to make sure you guys are good at this. That's it for this one. Let's keep going.
