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Rotational Motion

Up to now, we have only analyzed the dynamics of point masses that is objects whose spatial extent is either negligible or plays no role in their motion. Now, the type of motion which a point mass object can exhibit is translational motion that is motion by which the object moves from one point in space to another point. However, an extended object can exhibit another, completely distinct, type of motion by which it remains located more or less at the same spatial position, however, constantly changes its orientation with respect to other fixed points in space. This new type of motion is called Rotational motion. Consider a rigid body executing pure rotational motion that is rotational motion which has no translational component. So it is possible to define an axis of rotation for the sake of simplicity which is assumed to pass through the body, and this axis corresponds to the straight-line which is the locus of all points inside the body which remain stationary as the body keeps rotating. A general point located inside the body which is centered on the rotation axis and orientated in the plane perpendicular to this axis. To know rotational motion, you should be aware of the patterns of forces that cause rotation. Suppose for example, you and your friend face each other, standing on a slippery floor. You both hold your hands up at shoulder level, just assume. Then you hold his right hand with your left hand, and your left hand with his right hand. Then at the same time you begin to push on his right hand and pull on his left hand with the same force. So what’ll happen? If the floor is slippery enough, you'll both begin to rotate. Here you just notice that the two forces you're exerting on him are equal and opposite, so you might think according to Newton's Laws nothing at all would happen, even though you know better. But if you have knowledge in static equilibrium, you will find that there will be no change of motion if the forces add up to zero and if the forces act along the same point. Now if the forces don't act at the same point and result of their addition is zero, then the body acted on won't move away that means its center of mass will stay at the same position. But it will, in general, begin to rotate, until the frictional forces come into play to balance the applied forces on the body. Rotational motion in three dimensions is more complicated than planar rotation about a fixed axis, since the axis of rotation can change its direction. This type of rotation applies to bodies which experience three-dimensional motion. It is generally only necessary (and practical) to account for such rotation when determining the velocity and acceleration of a point on a body that is experiencing three-dimensional motion.

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