About dimension

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ONCE UPON (the matter arose at the beginning of our century), at a meeting of the academic council of the university, the head of the theology department spoke, who stated that physics students were very unserious about his subject, inattentive in lectures, and an outrageous example was given.

“I picked up one at the lecture, who himself did not push and did not give to others, and said to him: “Young man, I was just explaining what divine power is. Repeat! And he says: “Divine power is the product of divine mass and divine acceleration, the product will include the divine squared, therefore, to obtain divine power, only one of the collaborators must be divine.

This historical anecdote well illustrates the well-known rule: if, during calculations and transformations with naming, the dimensions of the left and right sides of the equation (or inequality) are different, then there is an error in the solution.

This rule often helps to remember the exact spelling of half-written formulas or physical laws. So, knowing that the formula for the period of oscillation of a mathematical matrix includes length (in cm) and acceleration of gravity (in cm/sec²), we can agree that to obtain the period in seconds, we need to divide the length by the acceleration and take the square root:

$$T = k \sqrt{\frac{l}{g}}.$$

We had to put $k$ because we don’t remember the formula exactly, and the dimensionless coefficient cannot affect its correctness. (Of course, dimension theory won’t help you remember that $k = 2\pi$.)

If you want to get acquainted with the “secrets of dimension” in more detail, we recommend that you read the small and accessible brochure by B. Yu. Kogan “Dimension of a physical quantity” (Nayka publishing house, 1968)

34

A positive review of a book is usually written like this.
First, briefly retell the content of the work,
note its advantages, some disadvantages
and finally, they recommend reading the book.
But you can do this in another way.
Here is a chapter from the book by G. I. Kopylov
“It’s all just cinematika.”
We will not praise the book
and advise you to read it.
We hope that after reading the above excerpt
you will do this, you must.

Mr. I. Kopylov