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How to Find the Height in a Uniform Circular Motion Problem

Trigonometry is the study of triangles, the relationship between their sides and angles, and the calculations derived from them There are three main trigonometric functions: sine, cosine and tangent. Each function relates an angle within the triangle to two of the three sides. Uniform circular motion refers to an object rotating around an origin at constant radius. As the object rotates about the origin, it creates a triangle, allowing the height to be determined using trigonometry.

Things You'll Need

Calculator
Ruler
Protractor
Paper

Instructions

- 1
  Determine the radius in the uniform circular motion problem. If this is a mathematics problem, a ruler may be needed to measure the radius of the circle or the distance between the moving object and the origin. Make a note of the radius.
- 2
  Measure the angle between the origin and the object using a protractor. To do this, line the protractor up with the origin and scan around the angles until the direction of the object is found. Make a note of the angle.
- 3
  Calculate the height. The lines between the origin and the object and between the object and the horizontal axis parallel to the origin, form a right-angled triangle and thus can be solved using trigonometry. To get the height, the sine function is used:
  
  Sin (theta) = height / radius
  
  Rearranged this gives:
  
  Radius x Sin (theta) = height.
  
  Hence in uniform circular motion, the height varies in a periodic fashion with angle Plug the values of radius and angle into the formula to obtain a value for the height.

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