# Rotational Motion and Angular Momentum

## Collisions of Extended Bodies in Two Dimensions


### Learning Objectives

By the end of this section, you will be able to:
1. Observe collisions of extended bodies in two dimensions.
2. Examine collision at the point of percussion.
Bowling pins are sent flying and spinning when hit by a bowling ball—angular momentum as well as linear momentum and energy have been imparted to the pins. (See ). Many collisions involve angular momentum. Cars, for example, may spin and collide on ice or a wet surface. Baseball pitchers throw curves by putting spin on the baseball. A tennis player can put a lot of top spin on the tennis ball which causes it to dive down onto the court once it crosses the net. We now take a brief look at what happens when objects that can rotate collide.
Consider the relatively simple collision shown in , in which a disk strikes and adheres to an initially motionless stick nailed at one end to a frictionless surface. After the collision, the two rotate about the nail. There is an unbalanced external force on the system at the nail. This force exerts no torque because its lever arm  is zero. Angular momentum is therefore conserved in the collision. Kinetic energy is not conserved, because the collision is inelastic. It is possible that momentum is not conserved either because the force at the nail may have a component in the direction of the disk’s initial velocity. Let us examine a case of rotation in a collision in .
The above example has other implications. For example, what would happen if the disk hit very close to the nail? Obviously, a force would be exerted on the nail in the forward direction. So, when the stick is struck at the end farthest from the nail, a backward force is exerted on the nail, and when it is hit at the end nearest the nail, a forward force is exerted on the nail. Thus, striking it at a certain point in between produces no force on the nail. This intermediate point is known as the percussion point.
An analogous situation occurs in tennis as seen in . If you hit a ball with the end of your racquet, the handle is pulled away from your hand. If you hit a ball much farther down, for example, on the shaft of the racquet, the handle is pushed into your palm. And if you hit the ball at the racquet’s percussion point (what some people call the “sweet spot”), then little or no force is exerted on your hand, and there is less vibration, reducing chances of a tennis elbow. The same effect occurs for a baseball bat.


### Test Prep for AP Courses


### Section Summary

1. Angular momentum  is analogous to linear momentum and is given by .
2. Angular momentum is changed by torque, following the relationship

 
  

3. Angular momentum is conserved if the net torque is zero 
        
           or


        
          

    . This equation is known as the law of conservation of angular momentum, which may be conserved in collisions.

### Conceptual Questions


### Problems & Exercises
