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Posted by: oldprof on 2010-03-03, 11:06:11
Some people will tell you there is no such thing as centrifugal force. That's total nonsense. It is as much a force as the force of your desk chair pushing on your butt. Like the push of your chair, the centrifugal force is a reaction force and it reacts to the centripetal force that causes the tangential velocity v to change heading as a body m rotates or revolves around an axis. So to answer your question.... Let f = ma = P - F; where P is centripetal force acting inward along the radius of turn and F is the centrifugal force acting outward along the turn radius. So when f = ma = P - F = 0, the radial forces are in balance and a = 0, which is the acceleration of the mass up/ down the radius. If that mass was at a fixed radius of turn, then as the forces are balanced, it would remain at that radius. For example, satellites remain in fixed radius orbits because the force of gravity P = F their centrifugal force. But if f = ma = P - F > 0, then a > 0 and the mass m would be accelerating inward toward the source of the centripetal force. For example, if a satellite puts on retro rockets and slows down a bit, its centrifugal force, which depends on its tangential velocity, lessens so that P > F and P - F > 0. The satellite will start to fall towards the gravity source... Earth. As the satellite's potential energy is converted into kinetic energy during its fall, the centrifugal force increases to a point where it once again balances the force of gravity P. The satellite will be again in a fixed, but lower altitude when this happens. And this is how controlled satellites can adjust their orbit altitudes. Works in reverse too. That is by momentarily boosting the tangential velocity and making F > P, the satellite will climb and trade the extra kinetic energy for potential energy at a higher altitude. Leaving just enough velocity and centrifugal force to offset the pull of gravity at the higher orbit. So, no, centripetal force is not always equal to centrifugal force. In fact, taken to the extreme, if the satellite came to a standstill, so that v = 0, there would be no centrifugal force, but the force of gravity, the centripetal force, would still be there. This, by the way, is why some like to say centrifugal force is not a real force. It does not exist without that tangential velocity; whereas, centripetal force can be attributed to one of the four fundamental forces of our universe. But, as I said earlier, it is as much a force as the force of your chair on your butt. If you feel that chair pushing on you, then it's a force and so is centrifugal force as it pulls on those satellites. |
