Circular Motion, Qualitative Description

Let's think a minute about a toy car moving along the floor and pretend the movement is frictionless. Figure 5-5 shows a top view, with the car moving to the right (see the motion marks behind the car). If we were to apply a rightward force FA, by blowing the car with a portable hair dryer, for instance, this would clearly speed up the car. If we were to apply a leftward force FB, this would slow it down. A force FC applied (for just a moment) perpendicular to the motion would neither speed it up nor slow it down, but it would cause the car to veer from its straight path.

Figure 5-5

If we are using a hair dryer to exert FC, then we can keep adjusting the direction of the force to keep it perpendicular to the motion of the car. The car will end up traveling in a circle (Figure 5-6). Given this discussion, the following box should seem reasonable.

Figure 5-6

If an object is moving at constant speed in a circle, then the net force on the object points toward the center of the circle, and the acceleration vector points towards the center as well.

In normal English, we do not say that the car is accelerating when it is turning. But in physics language, an object that is moving at constant speed in a circle is "accelerating toward the center of the circle", because the velocity vector is changing. We call this centripetal acceleration, which is Latin for "toward the center". (Parenthetically, "centrifugal" means "away from the center".) The force which provides the centripetal acceleration is the centripetal force.

Example-1

The Earth moves around the Sun. What force provides the centripetal force?

Solution

The gravitational force provides the centripetal force (Figure 5-7).

Figure 5-7

Example-2

A car goes around a curve to the left. What force provides the centripetal force?

Solution

This example is a bit more complicated. The driver turns her wheels to the left, so the wheels exert a force on the road to the right. By Newton's Third Law of Motion, the road exerts a force to the left on the wheels, turning the car left. In this case friction provides the centripetal force (Figure 5-8). (Think what would happen if there were no friction, for instance, if there were oil on the road.)

Figure 5-8

Example-3

A father is driving a car and turns to the left. There is a sack of groceries in the front passenger seat which crashes into the passenger door. The little brother Samson in the back seat asks the father why the groceries crashed into the door. The father says that was due to centrifugal force. The older sister Cadenza rolls her eyes at this, thinking about how much physics her brother will have to unlearn as he grows up. What is the correct explanation for the groceries' crashing into the door?

Solution

Figure 5-9 gives the real story. The groceries are going along a straight path, as we would expect according to the first law of motion. The car door is pulled into the path of the groceries. The father invents the word "centrifugal force" in order to hide his ignorance. Whenever you are tempted to explain something by centrifugal force, it is likely that you can explain it better with the ideas of first law of motion and a turning frame of reference (like the car).

Figure 5-9