9/25/2023 0 Comments Rotational motionIt doesn't matter what convention you choose, as long as you stick to it when adding up the effect of all the forces involved. We could count the leverage as positive if the force is tending to rotate the seesaw clockwise. It won't balance if both children sit on the same side of the middle. Actually, this definition needs to be made a little more precise, in that we need to keep track of which way the forces tend to rotate the seesaw. This leverage goes under several names: it is also called the torque, and sometimes the moment of the force. The two downward forces, the weights of the two children, both tending to rotate the horizontal seesaw, will cancel each other, so there will be no rotation, if they have the same amount of leverage, defined as the magnitude of the force multiplied by the distance from the center of the point where it operates. This is the principle of the lever, first spelled out by Archimedes. In other words, the 20 kg child must sit exactly twice as far from the center as 40 kg child, and the seesaw will balance. But we know from experiment that there will be no rotational motion if two children of different weights sit at different distances such that the ratio of the distances is the inverse of the ratio of their weights. This will also happen if two children of different weights sit at equal distances from the middle on opposite sides. If a child sits on one end, with nobody on the other end, the seesaw will certainly begin to rotate, and plonk the child down on the ground. Take the seesaw itself to be a uniform horizontal plank, with an axle through its midpoint, the balance point or fulcrum. Let's now analyze what's going on in terms of the forces acting on the seesaw. As everybody knows, this happens when the 20 kg child sits twice as far from the middle as the 40 kg child, assuming that the seesaw itself is balanced when nobody is sitting on it. Let's say we have a seesaw carrying two children, one weighing 20 kg and one weighing 40 kg, and that the seesaw is at rest, balanced. A familiar example of a body having forces applied at different points is the seesaw. To make any more progress, we need to find some quantitative criterion for when forces on a body, which do add to zero, are also in rotational equilibrium - that is, they won't cause the body to begin to rotate. But it will, in general, begin to rotate, unless frictional forces come into play to balance the applied forces. Even if the forces don't act at the same point, if they add to zero, the body acted on won't move away - that is to say, its center of mass will stay put. But if you look back at the notes on static equilibrium, the statement was that there will be no change of motion if the forces add up to zero and if the forces act at the same point. Notice, though, that the two forces you're exerting on me are equal and opposite, so you might think Newton's Laws would predict nothing at all would happen, even though we know better. What happens? If the floor is slippery enough, we'll both begin to rotate. Then at the same time you begin to push on my right hand and pull on my left hand with the same force. Then you hold my right hand with your left hand, and my left hand with your right hand. We both hold our hands up at shoulder level, say. For example, suppose you and I face each other, standing on a slippery floor. Before analyzing rotational motion, it's worth considering what patterns of forces cause rotation.
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