# 12.1 Motion along curved path

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Motion along a curved path can be analyzed in terms of circular motion.

We all experience motion along a curved path in our daily life. The motion is not exactly a circular motion. However, we can think of curved path as a sequence of circular motions of different radii. As such, motion of vehicles like that of car, truck etc, on a curved road can be analyzed in terms of the dynamics of circular motion. Clearly, analysis is done for the circular segment with the smallest radius as it represents the maximum curvature. It must be noted that "curvature" and "radius of curvature" are inverse to each other.

One common experience, in this respect, is the experience of a car drive, which is negotiating a sharp turn. If a person is sitting in the middle of the back seat, she/he holds on the fixed prop to keep the posture steady and move along with the motion of the car. If the person is close to the farther side (from the center of motion) of the car, then she/he leans to the side of the car to become part of the motion of the car.

In either of the two situations, the requirement of centripetal force for circular motion is fulfilled. The bottom of the body is in contact with the car and moves with it, whereas the upper part of the body is not. When she/he leans on the side of the car away from the center of motion, the side of the car applies normal force, which meets the requirement of centripetal force. Finally, once the requirement of centripetal force is met, the complete body is in motion with the car.

The direction in which the body responds to curved motion is easy to find by just thinking what would be the natural direction of motion of the free part of the body. In the example discussed above, the body seeks to move straight, but the lower part in contact with car moves along curved path having side way component of motion (towards center). The result is that the upper part is away from the center of curvature of the curved path. In order to keep the body upright an external force in the radial direction is required to be applied on the body.

## Negotiating a level curve

Let us concentrate on what is done to turn a car to negotiate a sharp turn. We realize that the driver of a car simply guides the steering of the car to move it along the turn. Intuitively, we think that the car engine must be responsible for meeting the requirement of centripetal force. This is right. However, engine does not directly apply force to meet the requirement of centripetal force. It is actually the friction, resulting from the motion caused by engine, which acts towards the center of circular path and meets the requirement of centripetal force.

The body of the car tends to move straight in accordance with its natural tendency? Now, as wheel is made to move side way (by the change in direction), the wheel has the tendency to have relative motion with respect to the road in the direction away from the center of path. In turn, road applies friction, which is directed towards the center.

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