What dimensions of (time)−2 mean ?

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    Dimensions Mean
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Discussion Overview

The discussion revolves around the dimensional analysis of the equation d²x/dt² = -k/m x, specifically focusing on the implications of the dimensions of k/m being (time)−2. Participants explore the concept of dimensions in physics and how they relate to acceleration.

Discussion Character

  • Conceptual clarification
  • Technical explanation
  • Exploratory

Main Points Raised

  • One participant expresses confusion about why k/m must have dimensions of (time)−2, given that the left-hand side of the equation represents acceleration.
  • Another participant suggests that understanding dimensional analysis is crucial for self-study in physics.
  • A participant emphasizes the importance of checking units to avoid mistakes, explaining that in the SI system, dimensions are assigned to units such as length (L) and time (T).
  • A later reply confirms that the dimensions of acceleration are length/time², with SI units being m/s².

Areas of Agreement / Disagreement

Participants generally agree on the importance of dimensional analysis and the relationship between acceleration and its dimensions, but there is no consensus on the initial confusion regarding the implications of k/m's dimensions.

Contextual Notes

The discussion does not resolve the initial participant's confusion about the meaning of dimensions in this context, nor does it clarify the implications of k/m being (time)−2 beyond the basic definitions provided.

Physou
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I am self learning Physics From a course I read the following :
" .. d^2x/dt^2 = -k/m x The left hand side is an acceleration so k/m must have dimensions of (time)−2 .. "
I understand that the left hand is acceleration but why does it imply that k/m must have dimensions of (time)−2 ? I guess I also don't understand the meaning of "dimensions" here. Thank you very much.
 
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Google for "dimensional analysis" - this is something you'll have to learn very early in your self-study.
 
Dimensional analysis and units are one of the most important things you can learn. If you always check your units you will catch a lot of mistakes.

In a system of units, each unit is considered to have some dimension. For example, in the SI system the meter (m) has the dimension of length (L) and the second (s) has the dimension of time (T).

So what are the SI units and dimensions for acceleration?
 
Thank you very much for your help, I really appreciate ! I understand now that length / time squared are the dimensions of acceleration and its SI units are m / s squared
 

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