Center of Mass and Moment of Inertia

In summary, the conversation was about finding the center of mass and moment of inertia for a collection of mass points. The equations used were center of mass and moment of inertia. The attempt at a solution involved calculating the center of mass and using the formula for moment of inertia. However, the final answer was incorrect.
  • #1
sealedhuman77
15
0

Homework Statement



Find the center of mass of the collection of mass points in Figure P.12 and then find the moment of inertia of the system about an axis through the center of mass and parallel to the y-axis.


Homework Equations



Center of Mass
Moment of Inertia

The Attempt at a Solution



M1 = 1kg, r1 = (1i + 0j) m
M2 = 2kg, r2 = (4i + 0j) m
M3 = 3kg, r3 = (6i + 0j) m
Mass total = 6kg

X of CM = 1/6 (0 + 8 + 18) = 13/3 m
Y of CM = 1/6 (0 + 0 + 0) = 0 m

I = mR[tex]^{2}[/tex]
I = 6 (4.333)[tex]^{2}[/tex]
I = 112.6667 kgm[tex]^{2}[/tex]

The answer was wrong. Thanks for the help
 

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  • #2
moving it up
 
  • #3
moving it up again
 
  • #4
I wouldn't keep bumping this thread until your attachment has been approved. ;)
 

1. What is the Center of Mass?

The center of mass (COM) is a point in a body or system of bodies at which all of the mass of the system can be considered to be concentrated. It is the point where the body is perfectly balanced in all directions.

2. How is the Center of Mass calculated?

The center of mass can be calculated by finding the weighted average of the individual masses in a system. Mathematically, it can be represented as: COM = (m1r1 + m2r2 + ... + mnrn) / (m1 + m2 + ... + mn), where m represents the mass of each individual object and r represents its distance from an axis.

3. What is Moment of Inertia?

Moment of inertia (MOI) is a measurement of an object's resistance to rotation. It is dependent on the mass distribution of an object and its rotation axis.

4. How is Moment of Inertia calculated?

Moment of inertia can be calculated by integrating the mass distribution of an object over its entire volume. The formula for calculating MOI is: I = ∫r²dm, where r is the distance from the axis of rotation and dm is the mass element at that distance.

5. Why is Center of Mass and Moment of Inertia important?

Center of mass and moment of inertia are important concepts in physics and engineering because they help in understanding an object's stability, rotational motion, and energy distribution. They are also essential in designing and analyzing various mechanical systems, such as bridges, vehicles, and machinery.

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