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How to Calculate the Scattering Angle

Scattering is a physical process that involves change in the path of an object when it comes in contact with another object. For example, when a billiard ball hits another one at rest on the table, the path of the first one changes. As a result of this impact, the second ball also starts moving in some direction. The angle at which the first ball scatters off of the second ball is called the scattering angle. For simple objects, such as billiard balls, this angle can be easily calculated using physics laws of motion.

Instructions

- 1
  Draw a 6-inch long straight line on a piece of paper. Draw a small circle having a radius of about 1 inch on one end of the line such that the circle's center is on the line. This circle represents the body at rest. Note down its radius on the paper. Let us assume that the radius is 1 inch, that is R = 1 inch. Draw another circle at the other end of the line such that its center is 1/2 inch away from the line. Draw a line parallel to the first line and passing through the center of the second circle. Measure the distance between the two lines using a ruler. Call this distance b. Let us assume that this distance is 0.5 inch, that is b = 0.5 inch.
- 2
  Divide b by R using a calculator and call this number x. For our case:
  
  x = b/R = 0.5/1 = 0.5.
- 3
  Enter the value of x in the calculator and press INV and COS in succession to calculate the inverse cosine of x. Press the multiplication button (X) and 2 on the calculator and then press enter to multiply the answer with 2. The required scattering angle "theta" will be displayed on the calculator. For our case:
  
  theta = 120 degrees.

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