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

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SUMMARY

The center of mass, as defined in Calculus 3, is the specific point within an object where it can be balanced, analogous to balancing on a needle. This point is crucial for understanding how forces act on an object, as any force applied on one side is countered by an equal force on the opposite side. The center of mass is often referred to as the center of gravity. Mastery of this concept is essential for tackling related topics such as Moment of Inertia and Radius of Gyration, which involve complex iterated integrals.

PREREQUISITES
  • Understanding of Calculus 3 concepts
  • Familiarity with iterated integrals
  • Knowledge of Moment of Inertia
  • Basic principles of physics related to forces and balance
NEXT STEPS
  • Study the application of iterated integrals in calculating the center of mass
  • Explore the relationship between center of mass and Moment of Inertia
  • Learn about Radius of Gyration and its significance in physics
  • Practice problems involving balancing objects using the center of mass concept
USEFUL FOR

Students in physics and mathematics, particularly those studying Calculus 3, as well as educators and anyone interested in the principles of balance and force distribution in physical objects.

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In simple terms, what exactly is the center of mass as taught in Calculus 3?
 
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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".
 
HallsofIvy said:
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.
 

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