About the Methodology of Teaching the Moment of Inertia in Algebra Based Physics Course
AbstractIn university physics courses the moment of inertia is a new concept, which falls out from secondary school level. The article presents the discussion of how the moments of inertia can be treated without using calculus in algebra based introductory physics courses. The proposed methodology defined in algorithmic way is introduced: representing the initial object as sum of discrete N masses, that is transferring the problem from continuous to discrete one; providing summation over such a discrete system to calculate the moment of inertia of it (mathematical notion omitted); tending N to infinity , that is returning from discrete to continuous mode again to obtain (mathematical notion omitted). The proposed methodology relies on the summation techniques readily accessible to an algebra-based introductory physics class. In fact, what students are required to know from mathematics, are some of the formulas for sum of degrees of the natural numbers: (mathematical notion omitted). Deriving that is within the scope of students abilities: as prerequisite, all what they have to know is formula for the sum of arithmetical progression for the first N natural numbers, and the formulas for higher degrees can be obtained from it by simple recurrence technique. Based on few examples, it is shown how the proposed algorithmic methodology works in practice for situations of various shaped bodies.