An object that is in circular motion experiences more complex dynamics than one in a linear motion. The contrast between circular motion and linear motion is that particles experience different types of forces and their forces are radius-dependent with respect to a fixed axis within that body. In other words, an external force acting in a direction other that the original motion will result in a change in force sich that the force of any particle is different with respent to one another about a fixed axis within the same body.
An object experiences linear motion only if no external force acts upon it to shift from its original direction, The earlier chapter on Newton's Law of Inertia also states that a body at rest will stay at rest. What happens, then, when an object starts to rotate? In order to understand this situation beyond the centrifugal force that we have already discussed, we need to examine some general features of the object.
Let's begin by looking at a car that is traveling in a straight line. When the car reaches a bend (left turn), the driver makes a judgement and turns the wheel so as to follow the bend. If he decides that he wants to move straight, then he may continue to move straight and drive away from the bend of the road, which essentially means that he breaks away from the winding of the road. This however, by the virtue of his original state of motion, does not require extra force-assuming that there is no centripetal force acting on the car. In fact, by turning the car actually causes a change in velocity, which in turn causes an acceleration towards the center. This creates centripetal force and thus, centrifugal force. Centrifugal force is in this context the force to move in a straight line. In another words, the car has nowhere else to go but to follow the path of the road, which is a bend. The analogy in this context is that the car has an option of traveling forward or takes the bend. So if the car chooses to take the straight road, the force will only be a linear component . But if it chooses the bend, then there will be extra components of the forces governing the motion. These competitive forces will decide the ultimate resultant force for that motion.
If we expand our example a little, let's assume that it is a long road and the driver has no idea that it is bending. The road will appear to the driver to be straight, and the driver continues to drive in the same manner as before. Because the bend of the curve is so minimal, he hardly feels any of thecentripetal force that is acting on him. Together with the fact that the road appears to be straight, he will conclude that the road is straight. Little does he know that hew was traveling tangentially on a huge circle! Simply speaking, he is traveling on a straight road at the point of the curve. This is somewhat similar to our daily experience with gravity and the rotational motion that we are in. We don't really "feel" it even we know it is there. While this notion may seem ambiguous at this stage, it explains the first component of a particle in circular motion which is going to be helpful when we go further.
Next, we look at a particle (our car, again) in a restricted frame. Imagine the above scenario, but this time including a motorcycle in the inner lane traveling parallel to the car. As the car makes a left turn, the motorcycle, in order to avoid a collision (anti-collision), will have no choice but to make a left turn along the bend as well. This is what I mean by the rotational motion of a particle in a restricted frame. In contrast to our earlier discussion about the car's option of going straight or making the curve, a particle that is traveling in a solid state is not only constrained by the direction-as in the case of the car and the motorcycle-but also by the velocity that is traveling within that frame. Relatively speaking, in a rigid body-be it a rod or sphere- the velocity (angular or tangential) of a particle cannot be faster than another particle that is further than the former from the center of rotation. this should be true provided that, other thing being equal, no additional force is impressed on it.
Now let's consider what actually causes a car to turn. You can say it the wheel of the vehicle that allows the car to turn, which is partly true. But the real kinematics behind that turn is that the front wheels of the car have actually decided to take a different direction and a shorter path against the original path. By changing the angle of the wheel, the right side of the car will take a longer route and the left sided will have a shorter route to travel (see fig.2). However, the acceleration is the same for both sides of the front wheels. In such a case, the wheels will not be able to achieve a position of equilibrium at this point of time. As mentioned earlier in our anti-collision analogy, which will bring about a change of velocity in both set of wheels, which then causes the car to turn. If the turning os too acute, as in the case of a car traveling at high velocity, both wheels will not agree on the direction or else the car will be out of control, as different side of the car will try to take a different route with a different velocity. Fortunate.y, modern roads are made to bend in a gradual manner so that the frictional force between the tires and the ground is able to counter this centrifugal force and maintain stability while the car is turning. For discussion purposes, if we suppose that only one wheel is made to turn, leaving the rest of the wheels going forward, what will be the resultant motion of the car then?
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