Can anyone give me a remedial explanation of centrifugal and centripetal force and examples of each at work?
Is the gravity on earth determined entirely by the mass of the planet, or do these forces contribute to it as well? To what extent?
If the rotation of the earth slowed by 50%, could we achieve gravity closer to that of the moon?
It all comes down to inertia. Inertia is the property of mass that resists change in motion. To physicists, change im motion is called acceleration, and all acceleration is caused by a force. F=ma
The principle of inertia often stated as “A body at rest tends to remain at rest, a body in motion tends to remain in motion,” but that leaves out the important concept of uniform motion. In other words, the “tends to remain in motion” part only applies if the motion is in a straight line at an unchanging speed. If you understand the vector nature of the term, unchanging velocity covers both.
So, what about things that are going around in circles? They would tend to go in a straight line unless acted upon by a force. Consider the case of a weight on the end of a string, being whirled around your hand. You can feel the weight pulling against the string, and you have to pull back to keep the weight going in a circle, even if you aren’t trying to get it to go any faster. That’s because you are changing the uniform motion from a straight line into a non-uniform curve, which is an acceleration, which requires force.
The force the string exerts on the weight, since it is directed toward the center of rotation, is known as centripetal force. It is a true force that causes the curve in the weight’s motion.
The force the weight seems to exert on the string, which attempts to cause the weight to travel in a straight line, is called centrifugal force. It is not a true force, since it is just a result of the weight’s inertia. It doesn’t cause any change in the natural uniform motion, so it isn’t causing acceleration of any kind. Therefore, it doesn’t fit the definition of a force.
On the earth, the gravitational pull of the planet acts as a centripetal force, pulling all the objects on earth toward the center, and into a curved path around that center. The inertial centrifugal force counteracts this a little, with the result that you weigh less at the equator than at the poles.
If the rotation of the earth slowed by 50%, there would be less inertial counteraction of gravity, and everything would weigh a bit more. To reduce the action of gravity, it would have to spin faster, and even then the effect would drop off as you went north or south.
I’m here without my reference books, so I can’t give you figures.
Centrifugal Force is the “fictitious force” that you experience when you’re in a rotating coordinate system. The Centripetal acceleration is what is keeping you moving in a circle, usually applied by the walls and floor of whatever you’re in. Your mind tends to think of your reference frame as the “fixed” system, so it seems as if some mysterious outside force is pushing at you when, for instance, your car makes a sharp turn. What’s really happening, of course, is that your body is trying to continue moving in a straight line. Your car is turning, and your mind thinks that your body should be turning with the car. But in order to do so, the upholstery has to push you in the right direction. That’s where you get the feeling of Centrifugal Force.
If you’re turning in a circle of radius R at a speed V, the magnitude of this force is MV2/R. (The V2 is supposed to be V squared. M is your mass).
This force is certainly present in the earth. t’sd why the earth bulges in the middle. The surface follows the isopotential, roughly, so that he sum of the “centrifugal” force and gravitational force is always perpendicular to the surface.
I think you have it backwards about the spin. The earth would have to spi FASTER, not slower, to reduce the apparent force of gravity. Considering that the force of gravity on the moon is 1/8 that on the earth, you’d have to spin pretty fast. I think we’d have other problems, then.
I was gonna post, there’s no real need. CalMeacham nailed it.
If it’s not clear from the foregoing, centrifugal and centripetal forces are two sides of the same coin.
Consider a ball on string that you are whirling in a circle over your head. Your finger feels a force pulling it outward, “away from the center”; the ball feels a force pulling it inward, “toward the center”. It’s the same force (the tension in the string), and whether it’s centripetal or centrifugal depends on your point of view.
Pluto is quite correct: centripetal and centrifugal forces are the same effect, viewed from different frames of reference.
To clarify, atop my previous gush:
Say you are driving a motor home, and you have a marble sitting on the flat table in the back. When you’re cruising along at 60 mph in a straight line (on an impossibly smooth road! :)), the marble will just happily sit there.
Make a left-hand turn. As you sit there watching the table, the marble will start rolling to the right, and will likely fall off the table.
What force acted upon it to make it do that? No force at all. The marble is simply continuing in a straight line like it had been - the vehicle is turning and moving out from under it. Since the rolling friction between the marble and the table is quite low, the table wasn’t able to drag the marble along with it in the turn.
This is why centrifugal force can be thought of as a “phantom” force. If you’re inside the vehicle, that’s where your reference frame is centered, and there seems to be some force acting on the marble, you, and the drinks in the fridge pulling to the right as the vehicle turns left. In reality, though, there is no force pulling you to the right - that’s simply your inertia at work. You hang on to a rail, and get help from friction on your butt, which is actually dragging you to the left.
Think of sitting on a freeway overpass watching this happen beneath you. From your perspective, the vehicle and its passengers are all simply turning left. If you had magical x-ray vision, you’d see the marble on the table simply continuing in a straight line.
Sitting on the overpass, you’re in a stationary (WRT the earth) reference frame - normal rules of inertia apply. A rotating reference frame (such as a turning vehicle) is non-inertial, and trying to blindly apply (i.e., without the corrective a[sub]rel[/sub] term) laws of motion in that reference frame will give you misleading predictions.
Also, some folks will try to tell you that centrifugal force is “wrong” in some way, and that the correct term is centripetal. This is silly. If you’re in a rotating coordinate system, such as the Earth, it often makes things simpler to pretend you’re at rest and consider the fictitious forces. You’ll get the exact same answer as you would if you converted to a non-rotating coordinate system first. If it works, use it.
I learned this in Physics in high school, but I see centrifugal force referred to all the time. You would think that, eventually, people would stop talking about it. Of course, we still say that the sun rises and sets when we all know that it doesn’t do either.
As Cecil points out…
http://www.straightdope.com/classics/a961122a.html
…gravity is a function of mass.
The forces you are talking about can affect your weight, but the gravity of the Earth is unchanged (the mass of the Earth and your mass are unchanged).
>> If the rotation of the earth slowed by 50%, could we achieve gravity closer to that of the moon?
If the rotation of the earth slowed by 50% the days would last 48 hours and your workday would feel like an eternity. But your commute would take the same time and your wife would be just as fat.