Find Physical Dimension of Constant C2

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Homework Help Overview

The discussion revolves around determining the physical dimension of the constant C2 in the context of an equation involving time and mass. The equation presented includes a term with a cosine function, which raises questions about the dimensionality of its argument.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between the argument of the cosine function and its dimensionality, noting that angles are dimensionless. There is an emphasis on understanding how the constants relate to the overall equation.

Discussion Status

Some participants have provided clarifications regarding the nature of angles in trigonometric functions, suggesting that the argument must be dimensionless. The discussion appears to be progressing with participants expressing appreciation for the insights shared.

Contextual Notes

There is a focus on the specific constants C1 and C2, with an acknowledgment that the original poster is comfortable with C1 but seeks clarity on C2. The nature of the equation and the role of time and mass are central to the inquiry.

AmrAmin
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hi, I have to find the dimension of the constant C2. I have no problem with finding constant C1. Here is the question, and I appreciate your help.

the equation is :

m= [tex]\sqrt{\frac{2t}{C1}}+m cos(\frac{1}{C2}t)[/tex]


I would like please to understand the solution with knowing the exact answer.
 
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AmrAmin said:
m= [tex]\sqrt{\frac{2t}{C1}}+m cos(\frac{1}{C2}t)[/tex]

The argument of a trigonometric function, such as (t/C2) here, is expressed in radians (or degrees), which is considered to be a dimensionless value. Recall that angle is defined on a circle as the arclength along the circle (s) divided by the radius of the circle (R); thus (theta) = s/R , making the radian a dimensionless unit.
 
Hint: Angles are considered dimensionless.
 
Thank you guys for making this is clear to me.
 

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