 
Many amusement park rides rely on circular motion to confuse your senses, to apply strong forces to your body, and to suspend your body in highly unusual positions ... all in the name of fun. Let's look at two typical rides that illustrate the concepts of centripetal force and acceleration from Physics 20.The ride at the right is a huge wheel which begins flat on the ground. A number of cages around the wheel hold riders, who stand. The wheel begins to turn, faster and faster. It's like standing on the rim of a large merry-go-round, facing inwards, that is spinning very fast. The cages keep you upright, and prevent you from being tossed into the souvenir stands.  Meanwhile, the entire wheel is being lifted into the air. To start, you are spinning around parallel to the ground; at the top, you are laying on your stomach looking down; at the bottom, you are laying on your back looking up (and fervently hoping that the people way above you don't pick this moment to lose their lunch...)As you lay in the cage, what you seem to feel is a force pushing you to the back of the cage. Even at the top of the spin, you have no sense of falling; you are being 'pushed' upwards into the back of the cage. It's the same 'force' you feel when you take a corner too fast in a vehicle, and are 'pushed' into the door beside you. This 'force' is commonly called 'centrifugal force'. There is no such force. Centrifugal force does not exist! 'Centrifugal force' is what you experience when you are moving. and a 'force' seemingly causes you to change direction. But no such force is involved. For example, imagine you are driving along the road. Suddenly the driver makes a sharp turn to the right. You find yourself 'pushed' into the door, and you say to yourself 'Aha! Centrifugal force!' Actually there was no force pushing you at all. Newton's first law tells us that objects that are in motion will stay in motion unless an unbalanced force acts on them. As you were moving along in the vehicle, and it turned, your body kept moving along in a straight line. Your body wants to keep moving in a straight line, and it will, unless something gets in the way. Let's make sure you've got it: There was no force that pushed you into the door. It was just your body continuing on down the road. Of course, within a second or two, your body encounters the door, as the vehicle turns and the door finds itself in your path. You hit the door. Here's what happens next: The door applies a force to your body to stop it. It continues to apply that force until the vehicle has completed its turn. This is the force that you feel. When the vehicle turns sharply, you don't hit the door ... the door hits you! Let's look at a different ride and make sure you've got the idea. 
Here's a roller coaster with a loop. It's a stand-up roller coaster ... all the better to see the fate that awaits you as you plunge down that first slope ...Some people must have a death wish!! O.K., imagine you're hurtling down the track, and hit this loop. You circle upside down ... what's the force that's holding you upside down at the top? ... centrifugal force, right? WRONG! Have you been asleep all this time, or what?!? There is no force holding you upside down. As you move along the track and the track curves uwards, the cars (and your body) want to keep moving in a straight line, and they try to. But the track curving upwards applies a force that pushes you into a loop. Here's a picture:  The yellow lines represent the straight path you and the cars want to continue following. The cars are moving very fast, so at some point, they want to head straight up! But the track continues to curve, applying a force and pushing the cars around. The question is not 'What's holding the cars up?'. The correct question is 'What's keeping the cars from flying straight up?'. The answer is the force applied by the track. This force is shown in red, at various locations around the curve. It's called the centripetal force, and its direction is always inward (perpendicular to the direction of motion). The cars are also accelerating ... not because they are changing speed, but because they are changing direction. This is centripetal acceleration, and its direction is the same as the centripetal force Fc. F = m·a and a = v2/r so Fc = mv2/r Incidentally, roller coaster loops are never perfect circles. If they were, the speed necessary to hold the cars to the track as they loop over the top would require 8 g's of acceleration going into the loop. This is much more than is tolerable by the human body ... fighter pilots often black out when experiencing 7 or more g's. (A 'g' is an acceleration that causes you to feel your normal weight. Eight g's would make you feel 8 times heavier). To eliminate this problem, ride designers make the loops in the shape of a clothoid, which is a curve where the radius is constantly decreasing as you move up the loop. This causes a higher centripetal force at slower speeds, and reduces the acceleration to 3 or 4 g's ... enough to make the ride exciting without injuring anyone. |