MHB What is the center of mass and how is it related to balancing an object?

[harpazo]

In simple terms, what exactly is the center of mass as taught in Calculus 3?

 

[HallsofIvy]

Imagine being able to balance an object from a needle supporting a single point inside the object. The "center of mass" is precisely that point. Any force on one side is balanced by a force on the other side. "Center of mass" is sometimes called the "center of gravity".

 

[harpazo]

Imagine being able to balance an object from a needle supporting a single point inside the object. The "center of mass" is precisely that point. Any force on one side is balanced by a force on the other side. "Center of mass" is sometimes called the "center of gravity".

The chapter in my Calculus 3 textbook does not have too many questions concerning the Center of Mass, Moment of Inertia and Radius of Gyration. The authors of the textbook state that each question involves iterated integrals and thus can be very intense and rigorous. I will post one or two questions for each topic. I want to clearly grasp this material before moving on to triple integrals.