 All right well it's time for some spring biking. One of the issues though when I'm biking is that I always get going so fast I end up slipping and falling. So we're gonna see if we can do a calculation to figure out the maximum speed that I can turn a corner at before I slip and fall. Here I am going down a cloud drive getting ready to go into the traffic circle. As I start to move in a circular path the force that keeps moving in a circle is the force of friction. So I can write the centripetal force is equal to the force of friction. Let's look at the calculation. When we're looking at an object on a horizontal surface making a circle this centripetal force is provided by the force of friction. So we can start by writing down fc equals ff. This is to find the maximum speed the bike will move at before it slides or it overcomes the force of friction. We can go to our formula sheet now and replace centripetal force with mv squared over r and force of friction with mu times the normal force. But how do we calculate that normal force? Let's take a look at a free body diagram of the bike viewed from the side. There's a force of gravity acting downwards on the bike and because it's on a horizontal flat surface like a road there's a normal force pointing upwards and those two forces are exactly the same size. There's also a centripetal force here but it's really hard to kind of draw and visualize because it's kind of going into the plane of the page so we don't really worry about that a whole lot at this particular view. You can see here that the normal force is the same as the force of gravity so that gives us a hint as to how we can substitute in for the normal force. The normal force on a horizontal surface is the same as the force of gravity so in place of normal force we could put mass times acceleration due to gravity. Now you'll notice that there's a mass on either side of the equation. It's the exact same value so those masses cancel out and now we can go and simplify the equation down. The speed we're looking for squared divided by the radius of the circle equals the coefficient due to friction multiplied by the acceleration due to gravity. All right well now let's collect some numbers and actually work out a speed. I went on google maps and recorded the radius of the circle at the traffic circle on the cloud av. It works out to 16.79 meters. Next I'm going to do some careful internet research to figure out what the coefficient due to friction for a bike tire and road is. It looks like it works out to about 0.7. Let's use 0.70 so we get two sick dicks. Now let's work it out. I'm going to make the centripetal force equal to the force of friction. In place of centripetal force I'm going to substitute in mv squared over r and in place of force of friction mu times the normal force. I can then replace that normal force with the force of gravity formula mass times acceleration due to gravity. The mass cancels out on either side and I can solve. So I'm going to put in for the radius of the circle 16.79 meters. The coefficient due to friction is 0.70 and the acceleration due to gravity. I'm not putting this in as a negative number since the centripetal force formula won't give us direction anyways it can only give positive numbers. This will work out to a speed to two sick digs of 11 meters per second. Okay we've got the ball on the rope again I'm going to spin it in a horizontal circle see how fast I can get it going before the rope breaks. So here I am spinning the ball in a horizontal circle. I need to pull in towards the middle of the circle in order to keep the ball moving in that circular path so I'm providing a force of tension through the rope. So the force of tension becomes the centripetal force in this situation. Alright let's work this one out. We're going to determine the maximum speed a 1.2 kilogram ball and a rope can rotate at if the rope is 1.5 meters long and the string can withstand a force of 150 newtons before it breaks. So here we're going to start off by saying that the centripetal force is equal to the force of tension. Tension is the force that makes the object go in a circle. In place of force of tension we can put in that 150 newtons and in place of centripetal force we can put in our formula mv squared over r. We also know what the mass of the ball is so we can substitute that in for m 1.2 kilograms. We're going to write down v squared and we're going to divide it all by the radius the circle makes which is the same as the length of the rope 1.5 meters. Do some algebra don't forget to square root and we're going to get a velocity to two significant digits of 14 meters per second. Now that we've tackled some horizontal circular motion in the next video we're going to try vertical circular motion. Pretty fast.