Uniform circular motion angle relationship

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Homework Help Overview

The discussion revolves around understanding the geometric relationships in uniform circular motion, particularly focusing on the properties of angles formed by lines that are either perpendicular or parallel. Participants are examining the implications of these relationships in the context of a diagram related to the problem.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning whether to focus on perpendicular or parallel lines, expressing confusion about the relationships depicted in the diagram. Some mention the use of similar triangles and reference geometric theorems related to angles with perpendicular sides.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the geometric relationships and expressing uncertainty about the relevance of the provided links. There is an exploration of different interpretations regarding the angles and their relationships in the context of the problem.

Contextual Notes

Some participants highlight the challenge of identifying parallel lines in the diagram, while others reference specific geometric theorems that may apply to the angles in question. The discussion reflects a mix of interpretations and attempts to clarify the geometric setup.

syllll_213
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Homework Statement
When reading the textbook, I was told the below marked angles are equal to each other, but I am not sure why because I am only familiar with the complementary and supplementary relationships of angles found in parallel line in math, but unsure how we derive this conclusion. For this free body diagram, I am assuming the same rule is used if we draw a line from the negative end of the x-axis to the force exerted by the weight?
Relevant Equations
angle = angle
Screenshot 2025-03-17 at 12.17.09 PM.jpeg
IMG_4DA82D3FB992-1.jpeg
 
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Hi, I am struggling to understand your response here. Should I focus on perpendicular lines or parallel? The link direct me to parallel line rules but I struggle to find any lines that have parallel relationship in the diagram.
Lnewqban said:
Note that the lines in question remain perpendicular to each other, rather than perpendicular, for any value of the angles that are equal.

Please, see:
https://www.mathsisfun.com/geometry/parallel-lines.html
 
Here is the geometry.
円中心角.jpg
 
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syllll_213 said:
Hi, I am struggling to understand your response here. Should I focus on perpendicular lines or parallel? The link direct me to parallel line rules but I struggle to find any lines that have parallel relationship in the diagram.
You can also use the concept of similar triangles (which happen to be right-angled triangles in this case).

https://www.mathsisfun.com/geometry/triangles-similar-finding.html
 
You can also make this construction:

1742181124627.png
 
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syllll_213 said:
Hi, I am struggling to understand your response here. Should I focus on perpendicular lines or parallel? The link direct me to parallel line rules but I struggle to find any lines that have parallel relationship in the diagram.
Mutually perpendicular.png
A useful theorem in geometry states that "Two angles with mutually perpendicular sides are equal." The free body diagram of a block on an incline on the right shows two such angles ##\theta.## The black side of one angle is perpendicular to red side of the other. If you decrease the angle of the incline to zero, the red line that is perpendicular to the incline will be along the vertical and the other angle ##\theta## will also be zero.
 
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