BR physics, rotations!

[anbuitachi]

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Hi im confused about this question.

So there's this cylinder thing spinning on earth's surface. where is the normal force exerted the greatest in it?

So it's obviously at the lowest point because of gravity and the rotation. However i'm confused about the mathematical answer given. It says at the top of the cylinder, mg, N, Fc are all pointing down, while at the bottom, Fc, N are pointing up and mg is pointing down. Yet when they right it, at the bottom they right N= mv^2/R + mg and at the top N=mv^2/R - mg.

I understand the equations but I don't understand the relation to the picture with the direction of the forces, they drew Fc pointing inward, yet in the equation it's pointing outward? So i guess i'm confused about the direction thing with Fc.

 

[muhali3]

Yeah, the centripetal force/acceleration vector is always a straight line from the center of the object to the center of whatever it is going around.

http://www.youtube.com/watch?v=GBGGh2Ie4d0

Khan academy is great at teaching this.

 

[anbuitachi]

yes i know that Fc points inward. However in the calculations the Fc points inwards but the math shows outwards. They gave N= mv^2/R + mg for the equation for being at the bottom. but gravity points down while Fc points up, and Normal also points up, so I dont understand why the equation isn't N + Fc = mg, with g being negative, resulting in N = -mg - Fc

 

[muhali3]

I answered this question conceptually but I will try to explain how the picture and equations both make sense.

At the bottom Fc is directly pointing up and there is also an "opposing force" to the weight force that is directly pointing up. These two components make up the normal force, and are both positive (pointing up) at the bottom, thus explaining the equation for the bottom. Normal force at the bottom is not the difference of Fc and Fw, but rather the sum. The normal force is providing Fc and providing a force that is "equal and opposite" to the weight force.

You also shouldn't think of the normal force and Fc independently. Fc is a result of the normal force, and Fc will be the same at any point in the cylinder. Any variation in the normal force will be due to the weight force. The equation for the normal force will always start with "N = mv^2/R...".

This is hard to explain without drawing the vectors out, and I get what you're asking, "why is Fc at the top positive and the weight force negative if they are both pointing down".

but yeah...anyways, I hope I answered your question.

 

[anbuitachi]

Still confused lol

You said "These two components make up the normal force, and are both positive (pointing up) at the bottom, thus explaining the equation for the bottom. Normal force at the bottom is not the difference of Fc and Fw, but rather the sum."

If both are pointing up, why is normal force the sum? I thought when you add forces (vectors) you add it based on direction. If both Fc and N are pointing up, shouldn't you add Fc + N = the force pointing opposite direction which is mg resulting in Fc + N = mg?

 

[muhali3]

Still confused lol

You said "These two components make up the normal force, and are both positive (pointing up) at the bottom, thus explaining the equation for the bottom. Normal force at the bottom is not the difference of Fc and Fw, but rather the sum."

If both are pointing up, why is normal force the sum? I thought when you add forces (vectors) you add it based on direction. If both Fc and N are pointing up, shouldn't you add Fc + N = the force pointing opposite direction which is mg resulting in Fc + N = mg?

The normal force is the sum of all forces being provided by the inside surface of the cylinder. You can't think of normal force independently of the Fw and Fc, because if there were no Fw and Fc, there would be no normal force.

If you think about a planet orbiting a star, the planet is undergoing centripetal force, but what is causing the centripetal force? The gravitational force. Fc would be a result of Fgrav, the two forces are the same thing. You wouldn't add Fc and Fgrav together to determine the total force inwards, because they're the same thing (Fg = Fc).

So with that understood, let's say the cylinder was not rotating, and something was on the bottom, what would be the normal force on that object? It would be +mg (equal and opposite to weight force). So without rotation we have N=mg.

So how do we deal with rotation? The inside surface of the cylinder is providing Fc, just as Fgrav provides Fc in space. So at the bottom, the surface is providing two forces, the centripetal force and +mg. If you think about normal force as the "surface force" then you will see that the normal force is made up of the "opposite" force and Fc. (N = mg + Fc)

You wouldn't do Fc + N = mg, because N is made up of mg and Fc.

If you still don't understand it, then you can watch those KhanAcademy videos, because that's how I learned it, it's only like 25 mins total and it will give you a very good conceptual grasp of it. This subject is not very intuitive.