In the previous chapter, three forces were discussed: weight, tension and normal force. In this chapter we will discuss in detail friction, drag, and centripetal acceleration. All of these forces are commonly observed in motion, and there are several real world examples of them. For instance, a race car must be engineered so that it encounters minimal friction with the track, as well as minimal air drag as it races. However, the tires of the car must be designed so that some friction is encountered. If the tires were frictionless, the car would not be able to slow down when making a high-speed turn, and would end up crashing.

## Types of ForcesEdit

In this chapter, we will focus on three other forces: friction, drag, and circular motion.

### FrictionEdit

Friction is a force that always opposes all motion; it always acts in a direction exactly opposite to that in which an object is moving (or trying to move), and typically comes when the object rubs or drags against another object as it moves. It is defined as where is the coefficient of friction, and is the normal force acting on the object. There are two types of friction, static and kinetic, also known as sliding friction. Static friction is the amount of initial force required to move an object, and kinetic friction is the amount of force required to sustain motion in an object. Because of this, static friction is always greater than or equal to kinetic friction.

### DragEdit

Drag is like friction in that it always acts in a direction opposite to that in which an object is moving, but comes from fluids such as air and water, through which an object might be moving. This relationship is documented in the equation , because the vectors representing drag and motion are in opposite directions. Since drag occurs in the presence of fluids, air resistance is a form of drag. Drag is related by the equation , where is the drag coefficient, is the effective surface area that encounters the resistance, is the fluid density, and is the object's speed.

### Circular MotionEdit

Imagine a person whirling a yo-yo around in circles. The yo-yo has a string of length 10 cm, and a constant speed. While the speed is constant, the velocity however, is not. This is because velocity has a direction, and in circular motion, the direction is always changing. An easy way to understand this is to think of a circle with several points on it. Using the points, draw tangent lines on the circle. These tangent lines represent the different velocities, all of which have varying directions, even though their speed may be the same. Remember that speed is the magnitude, or absolute value of velocity. A general equation gives the *centripetal acceleration* in terms of the velocity and the radius: