X Flashcards
What is the moment of inertia of an object?
It involves a continuous distribution of mass at varying distances from any rotation axis.
What mathematical discipline is generally used to calculate moments of inertia?
Calculus.
What is the moment of inertia of a point mass defined by?
dm
where dm is the differential mass element.
What is a differential element of mass?
An infinitesimal mass element dm.
What is the formula for the moment of inertia contribution by a differential element of mass?
dI = r²dm.
What does the ‘d’ in dI and dm signify?
It denotes a vanishingly small or differential amount.
What must the differential element of moment of inertia dI be defined with respect to?
A specific rotation axis.
What is the sum over all mass elements in the context of moment of inertia called?
An integral over the mass.
Fill in the blank: The moment of inertia generally involves a _______ distribution of mass.
[continuous]
True or False: The moment of inertia can be calculated without using calculus.
False.
