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Boundless Physics
The Basics of Physics
Solving Physics Problems
Physics Textbooks Boundless Physics The Basics of Physics Solving Physics Problems
Physics Textbooks Boundless Physics The Basics of Physics
Physics Textbooks Boundless Physics
Physics Textbooks
Physics
Concept Version 7
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Trigonometry

Trigonometry is central to the use of free body diagrams, which help visually represent difficult physics problems.

Learning Objective

  • Explain why trigonometry is useful in determining horizontal and vertical components of forces


Key Points

    • It is important to identify the problem and the unknowns and draw them in a free body diagram.
    • The laws of cosine and sine can be used to determine the vertical and horizontal components of the different elements of the diagram.
    • Free body diagrams use geometry and vectors to visually represent physics problems.

Term

  • trigonometry

    The branch of mathematics that deals with the relationships between the sides and the angles of triangles and the calculations based on them, particularly the trigonometric functions.


Full Text

Trigonometry and Solving Physics Problems

In physics, most problems are solved much more easily when a free body diagram is used. Free body diagrams use geometry and vectors to visually represent the problem. Trigonometry is also used in determining the horizontal and vertical components of forces and objects. Free body diagrams are very helpful in visually identifying which components are unknown and where the moments are applied. They can help analyze a problem, whether it is static or dynamic.

When people draw free body diagrams, often not everything is perfectly parallel and perpendicular. Sometimes people need to analyze the horizontal and vertical components of forces and object orientation. When the force or object is not acting parallel to the x or y axis, people can employ basic trigonometry to use the simplest components of the action to analyze it. Basically, everything should be considered in terms of x and y, which sometimes takes some manipulation .

Free Body Diagram

The rod is hinged from a wall and is held with the help of a string.

A rod 'AB' is hinged at 'A' from a wall and is held still with the help of a string, as shown in . This exercise involves drawing the free body diagram. To make the problem easier, the force F will be expressed in terms of its horizontal and vertical components . Removing all other elements from the image helps produce the finished free body diagram .

Free Body Diagram

The free body diagram as a finished product

Given the finished free body diagram, people can use their knowledge of trigonometry and the laws of sine and cosine to mathematically and numerical represent the horizontal and vertical components:

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