What is the meaning of the sum of tan A and rad A?

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Discussion Overview

The discussion revolves around the physical meaning of the sum of tangential acceleration and radial acceleration in the context of circular motion. Participants explore the implications of these concepts and their relevance to understanding total acceleration.

Discussion Character

  • Homework-related, Conceptual clarification, Technical explanation

Main Points Raised

  • One participant questions the physical meaning of the sum of tangential and radial accelerations, wondering if it serves merely as a mathematical tool.
  • Another participant suggests that the vector sum of the two orthogonal components results in the total acceleration of the body.
  • A different participant seeks clarification on the physical meaning of total acceleration, asking if it arises from the definitions of the two types of acceleration.
  • One reply states that total acceleration is simply the rate of change of velocity, implying a foundational understanding of acceleration.
  • Another participant explains that any particle moving along a curved path experiences acceleration, and that the components can be defined in various directions, but using tangential and radial components is conceptually clearer.

Areas of Agreement / Disagreement

Participants express varying degrees of understanding regarding the physical meaning of total acceleration, with some focusing on its mathematical representation and others on its conceptual basis. The discussion does not reach a consensus on the deeper implications of the sum of the two accelerations.

Contextual Notes

There are unresolved questions regarding the definitions and implications of tangential and radial acceleration, as well as the interpretation of total acceleration in different contexts.

Shing
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Today I was doing a homework that asked me to calculate the sum of some particular tangential acceleration and radial acceleration in a circular motion.

We all know clearly about the concepts independently, but I wonder what the physical meaning the sum of the two accelerations is? Or it is just a some kinda tool like math?

Thanks for reading
 
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Presumably they want the vector sum of those two orthogonal components, which gives you the total acceleration of the body.
 
so what is the physical meaning of the total acceleration?
Is it something produced by the two accelerations' definitions?
 
It's the rate of change of velocity. Just the plain old regular acceleration that you've hopefully learned about before...
 
Basically, any particle undergoing a curved path has an acceleration (which is what allows it to curve) - the components of the acceleration could have been taken in any direction not orthogonal to the acceleration, but since we have a conceptual basis of perpendicular to the path and tangent to the path, its easier to give the components in terms of those directions.
 
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