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One of the simplest, yet most powerful, tools in the physicist’s bag of tricks is dimensional analysis1. All quantities of physical interest have dimensions that can be expressed in terms of three fundamen-tal quantities: mass (M), length (L) and time (T). We express the dimensionality of a quantity by enclosing it in square brackets.
28 Μαΐ 2013 · Here are three ways to describe the formula of a line in $3$ dimensions. Let's assume the line $L$ passes through the point $(x_0,y_0,z_0)$ and is traveling in the direction $(a,b,c)$. Vector Form $$(x,y,z)=(x_0,y_0,z_0)+t(a,b,c)$$ Here $t$ is a parameter describing a particular point on the line $L$. Parametric Form $$x=x_0+ta\\y=y_0+tb\\z=z_0 ...
Find the dimensions of a mathematical expression involving physical quantities. Determine whether an equation involving physical quantities is dimensionally consistent. The dimension of any physical quantity expresses its dependence on the base quantities as a product of symbols (or powers of symbols) representing the base quantities.
Find the dimensions of a mathematical expression involving physical quantities. Determine whether an equation involving physical quantities is dimensionally consistent. The dimension of any physical quantity expresses its dependence on the base quantities as a product of symbols (or powers of symbols) representing the base quantities.
Find the dimensions of a mathematical expression involving physical quantities. Determine whether an equation involving physical quantities is dimensionally consistent. The dimension of any physical quantity expresses its dependence on the base quantities as a product of symbols (or powers of symbols) representing the base quantities.
Exercise 2(c) We want to check the dimensions of the equation E = mc 2. Since E is an energy it has dimensions ML T−2. The right hand side of the equation can also be seen to have this dimension, if we recall that m is a mass and c is the speed of light (with dimension LT−1). Therefore [mc2] = M(LT−1)2 = ML2 T−2
Rearrange the equation to find an expression for in terms of the other variables. Then, equate the dimension of to that of the right-hand side of the equation. Find the dimensions of each term in the expression, and then combine them using products and quotients where appropriate.
