 Welcome to the Batcave, which is actually just my garage. I've been thinking about Batman, he is the coolest superhero because he knows so much about physics. I mean just think about it, he's got this bat-erang on the end of a rope and he spins it around in a vertical circle. How does he know how fast to spin that, the minimum speed he needs to keep it going in a circle. So here I am ready to get out my patented bat-erang and start going in a vertical circle. I'm going to see if we can figure out the minimum speed needed to keep that bat-erang in a vertical circle. Now that minimum speed is going to occur at the top of the circle because at that moment in time when the things at the very top you're going to have no tension in the rope. The only thing needed to keep it moving in a circle at that point is just the force of gravity. If you've ever swung something in a circle you kind of know at the top of its path it doesn't even feel like that it's pulling on that rope any, that's because the tension is zero at that point. Mathematically we can now say that the centripetal force is equal to the force of gravity. We can replace that centripetal force with mv squared over r, that formulas on our last video, and we can take a look at the force of gravity as being mg. The mass on either side is the mass of the bat-erang and that cancels out. That's going to leave us with v squared over r equals acceleration due to gravity. You know what's great about that last calculation is there's another question where you do the exact same calculation in this topic. Let's think about if Batman was doing a loop-the-loop roller coaster style trying to figure out the minimum speed he needs to maintain that circle so he doesn't fall off at the top. When a roller coaster car moves in a vertical circle the forces that make up this centripetal force are the normal force and the force of gravity. But if you're looking for the minimum speed needed to keep that object at a circle then the normal force is zero at the top of the track at that minimum speed the very slowest you can go without falling off the track. So that means we can use the exact same series of steps making this centripetal force equal to the force of gravity cancelling out the masses and ending up with that same calculation. That math will work for both of these situations. And lastly let's go back to that vertical battering again. What's the fastest you could spin the battering before the rope breaks? Last video we saw how fast you could swing an object on a rope in a horizontal circle before the rope broke. We saw that all we had to do there was make this centripetal force equal to the force of tension. But what about if it's a vertical situation? Well now what we need to do is start to think about the force of gravity as well. The position where this rope is going to break is at the bottom of the circle because at the bottom of the circle we have sort of a tug of war between the force of gravity pulling down and the force of tension from Batman pulling up. So we're going to take a look at this situation now and see if we can deal with these two opposite direction forces to work out the maximum speed. Let's look at an example from the notes. Here the force of tension the rope can hold before it breaks is 135 newtons, the mass of the object is 2 kilograms and the length of the rope is 1.10 meters. We make a free body diagram. We've got a centripetal force towards the middle of the circle and a force of tension that's me pulling up on that rope as the object's at the bottom of the circle. There's also a force of gravity pulling down on the object as well which is what makes it different from the horizontal situation we looked at in the last video. The centripetal force here will be equal to the force of tension plus the force of gravity together. There's two forces here making up this centripetal force. In place of centripetal force I can still put mv squared over r and in place of force of tension well nothing to put in there there's no formula for tension and force of gravity is mg. Now I can substitute in my mass and I can substitute in the length of the rope which is the same as the radius of the circle that the batter angle make. I'm going to substitute in my force of tension I had in the question and I'm going to substitute in the mass again and the acceleration due to gravity. Now one of the things you've got to be really careful with in this situation is making sure you have that acceleration due to gravity as a negative number. Why are we going to put that as a negative? Well because we're looking at a force of gravity that's pointing downwards and this is one of the big differences between the horizontal and vertical situation. In the horizontal situation everything was positive. So I'm going to get a velocity of 7.97 meters per second. I'll be right there commissioner. The bat pulse. Yes commissioner. Right away. To the bat pulse. To the bat pulse.