Which equations are dimensionally consistent

Checking equations routinely by dimensional analysis save us the embarrassment of using an incorrect equation. Also, checking the dimensions of an equation we obtain through algebraic manipulation is a great way to make sure we did not make a mistake or to spot a mistake, if we made one. One further point that needs to be mentioned is the effect of the operations of calculus on dimensions.

We have seen that dimensions obey the rules of algebra, just like units, but what happens when we take the derivative of one physical quantity with respect to another or integrate a physical quantity over another?

The derivative of a function is just the slope of the line tangent to its graph and slopes are ratios, so for physical quantities v and t , we have that the dimension of the derivative of v with respect to t is just the ratio of the dimension of v over that of t :. Similarly, since integrals are just sums of products, the dimension of the integral of v with respect to t is simply the dimension of v times the dimension of t :.

By the same reasoning, analogous rules hold for the units of physical quantities derived from other quantities by integration or differentiation. A student is trying to remember some formulas from geometry. Determine which formulas are dimensionally consistent. Yes, both terms have dimension L 2 T -2 b. Yes, both terms have dimension LT -1 d. Yes, both terms have dimension LT Privacy Policy. Skip to main content. Search for:. If you forgot your password, you can reset it.

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Email Required, but never shown. Featured on Meta. In fact, it seems reasonable to suppose that depends principally on the mass of the tower, , the height of the tower, , and the acceleration due to gravity,. See Fig.

In other words, 5.