Three questions, and thanks in advance to whoever answers them!
1. I was reading the NOVA book, and it said that the normal force is not always equal to mg or gravitational force. In what instances would this be true? Some examples please...
2. How do you determine the direction of torque? Is it simply clocks are negative, and a positive value= counterclockwise, and negative value = clockwise direction?
3. Is there a simpler way to understand right hand rule #1?
It says your fingers should point in direction of B, and your thumb in the direction of velocity? What if angle between v and B is 150? Then which direction would your thumb be pointing? And are there only 4 directions for the force: up, down, into the page, and out of the page?
1.
-Imagine a block such that it rests on a flat surface while a rope provides some vertically upward tension (i.e. the rope is affixed to suspend the block somewhat). Here, the normal force is equal to the gravitational force minus the tension in the rope.
-In outer space, free of the force of gravity, imagine a collision between two asteroids. When the two objects collide, they exert a normal force on one another.
-Imagine two magnets with a wooden block between them in outer space, free of any gravitational forces. The magnetic force causes the two magnets to attract each other, and four normal forces arise. Each side of the wooden block exerts a normal force against the magnet that is equal in magnitude but opposite in direction of the magnitude of the magnetic force that each magnet exerts on one another, adding for a total of two normal forces on the magnet due to the wooden block. In addition, each magnet exerts a normal force on the block, for a total of two additional normal forces on the wooden block due to each magnetic face that is in contact with the block (two faces total, one from each magnet).
I don't know your understanding about the normal force in general, but let me say this: The normal force is actually an electrostatic force. It comes from the Pauli exclusion principle, which disallows electrons with parallel spins to fill the same orbital levels. In other words, the normal force has nothing whatsoever to do with gravitational force per se, but the force of gravity can trigger the occurrance of the normal force.
2.
Torque is a vector valued definition. Torque equals r cross F, where r is the radius from the chosen origin (the point about which angular motion occurs), and F is the force on the object. Using the right hand rule, we can find the direction of the torque. Your guesses of clockwise or counterclockwise are non-sensical. Torque has no simple direction; you must always find it with the right hand rule (R.H.R.).
3.
Here is my version of the right hand rule. If you are crossing two vectors, A cross B, point your index find in the direction of A and your middle finger should bend until it is aligned with the direction of B. (WARNING: You MUST ensure that the two vectors, A and B, are joined at the tail before doing this procedure.) Then your thumb will naturally point in the direction of the vector that represents A cross B.
if the angle between v and B is 150 (degrees presumably), then just follow the aforementioned rule.
There are 6 basic directions from the origin in cartesian coordinates: +x, -x, +y, -y, +z, and -z. When you said, "up, down, into the page, and out of the page" you forgot left and right. Any direction can be a combination of these directions as well.
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