Each of the mathematical expressions below was given by a student on his or her way to the solution of an exam problem. Assume each of the symbols stands for what we use them for in this class (as indicated in each line). If you believe the equation given could possibly be a correct physical equation, indicate Y . If you think that it could not possibly be a correct physical equation, indicate N and give a brief explanation of why you think so.

(a)	(mass, gravitational field strength, coefficient of friction, normal force)
(b)	(tension, mass, gravitational field strength, moment of inertia, radius)
(c)	(force, pressure, area)
(d)	(velocity, universal gravitational constant, mass, radius)

Solution

None of the equations are legitimate. Here are the dimensional analyses.

(a) [mg] = [N] = [Force] = ML/T². [m] =1 (i.e., is dimensionless).

(b) [T] = [mg] = [Force] = L/T²; but [I]=[MR²], not = [MR] so [I/MR] is not equal to [1].

(c) The left side is a vector, the right side is not. The dimensions are OK so the correct form of the equation would put a vector over the A (the normal to the area).

(d) Since [GMM/R²] = [Force] it must hold that [GM/R] = [Force R/M] = (ML/T²)(L/M) = L²/T² so it's square root can equal velocity. This one works.

Page last modified September 6, 2004: G13