**Concept:** How to Solve: Energy vs Torque

Hey guys! Now that you've solved a bunch of rotation questions using energy and a whole bunch other questions using torque, you might have noticed that some of these questions are very similar. For example, we did yoyo equations for both energy and torque. What I want to do in this video which is really critical is do an overview of these two methods so you know which one to use in different situations. Let's check it out. I want to remind you real quick that some linear motion problems, we could solve them using either F = ma and motion equations. Remember, we have those three to four motion equations, kinematics equations. 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. Most people learned this one first and then they learned this one. 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 three to four motion equations to pick from. I want to show you this in linear motion and then we're going to bring it back to rotation real quick. If you have a block here and the block slides on an incline and let's assume that'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's two ways. The first way, I'm going to use the first way here to be F = ma in motion equation. The first way would be with motion and what you would do just like any motion problem, you would list your variables Ð V initial, V final, a, _x, _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, _x and _t. Let's say we have the initial height, so any angle. Let's say these are given. From these, you would be able to find your _x because h = _xsin_. If I give you these two, you can find this one. You would have some _X as well. You wouldn't have __. That would be your ignored variable. But notice that to solve this, you need to know two things. You would know V initial. You could find _X. You would be missing acceleration. What you would do to find acceleration is you would write sum of all forces equals ma. 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. When I write sum of all forces in the x axis, I have mgx = max. mgx is mgsin_ and equals ma. We're just going to call it a. The masses cancel and I'm left with an acceleration. At this point, I know the acceleration. I can plug it in here. I know the acceleration, I can plug it in there. I can use the fact that my ignored variable is _t to know that I have to use the second equation which is V final^2 = V initial^2 + 2a_x. It's the only equation that doesn't have _t. I can solve here, I can cancel this out and the final velocity would be the square root of two. The acceleration is right here, gsin_ and I have _x. I can rewrite _ X if we want to. Notice that if I rewrite _x is h/sin_. If I do this, look what happens. The sines cancel and I have that the final velocity simply the square root of 2gh. You could do this using a combination of motion equations and F = ma. Kind of long. It's much better to do this 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 mgh initial. Work non-conservative is the work done by you. You're not doing anything, you're just watching plus the work by friction. There is no friction so this is zero. At the end we have kinetic energy because we have linear motion, so this is _ MV final^2 and there is no potential energy at the end because you're at the lowest points. We cancel the masses and V final is the square root of 2ghinitial. This height here is obviously the initial. I end up at the same place. Given the choice of methods, you would obviously choose the energy way of solving things because it is better. 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's two ways to solve problems, we're going to have the same thing in rotational motion. Some problems instead of being solved in rotation, instead of being solved with F = ma in motion equations, would be solved with Torque = I _ in motion equations. 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 because it's easier. But it really depends on what you're being asked or what you're being given, or actually and on what you're being given. Generally you will use Torque = I _ if you're either being asked or given a or _. 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 _. You're always going to use motion equations if you're looking for time _t or if you need time to solve the problem somehow. You're always going to need motion equations. I think this is really important to remember and it helps a lot 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. If you could have used an easier method, sometimes a question will say, ÒUsing Newton's laws which means F = ma or Torque = I _, do this.Ó What professors will do sometimes is force a method upon you to make sure that you can't use an easier method. I want to do a quick example here of how questions may look almost identical but require different methods to solve. A yo-yo spins around itself as it falls, something like this. The yo-yo is falling and spinning at the same time. It has an a and a v and it has an _ and _. 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. We would have to use to find acceleration a combination of F = ma, Torque = I _. The fact that it drops 2 meters doesn't matter. The acceleration is constant throughout. This is just extra information. By the way, the reason to use both of these is because a yo-yo has linear acceleration and angular acceleration at the same time. Here we want to know the speed after dropping 2 meters. Both pieces of information are important and we're going to use energy. Then here we want to know how long does it take to drop 2 meters. Drop 2 meters is _y and how long does it take is _t. Because I'm being asked for time, you have to use motion equations. But it's very likely that motion equations is not going to be enough because to do this, 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 _y and you're looking for _t. You're going to have to either find V final using energy or you're going to use F = ma and Torque = I _ to find acceleration so that you can use motion equations. Here to solve this, you're going to use motion and either F = ma or energy, depending 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. I think this is crucial for you to master. I hope it makes sense. 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.