how to dimensionaly analys ML=MLcos(LT)'
To dimensionally analyze the equation ML = MLcos(LT)', the first step is to identify the dimensions of the variables involved in the equation. Let's break down each term:
ML - This represents a variable with the dimension of mass times length (M*L).
cos(LT)' - To determine the dimension of this term, we need to decompose it further:
cos - This is a trigonometric function, and thus it is dimensionless.
(LT)' - This term involves both length (L) and time (T). Since (LT)' is in the argument of the cos function, we can assume it represents an angle. An angle is a dimensionless quantity.
Now, to dimensionally analyze the given equation, we equate the dimensions on both sides:
ML = MLcos(LT)'
The dimension of ML on the left side is M*L, and the dimension of MLcos(LT)' on the right side is also M*L, since both cos(LT)' and ML are dimensionless.
Therefore, the equation is already dimensionally balanced.
In summary, the given equation is already dimensionally balanced and does not require any further dimension analysis.