I think we'll want to see a diagram or better description of the orientations, placement, and dimensions of the objects. We shouldn't have to fish about in your solution equations to find the statement of the problem.Ella Tankersley said:
I added a diagram, can you see it?gneill said:
Ah! Much better! Thanks.Ella Tankersley said:
I don't understand this calculation. Why is the plate at z = 0?Ella Tankersley said:
I was assuming that the plate is very thin so there is no thickness in the z directiongneill said:
What has the plate's thickness have to do with its center of mass position with respect to the xy plane?Ella Tankersley said:
Ella Tankersley said:
To calculate the z component of the center of mass of a complex shape, you need to divide the moment of inertia about the z-axis by the total mass of the object. This will give you the distance from the z-axis to the center of mass.
Finding the z component of the center of mass is important because it helps determine the stability and rotational motion of an object. It also allows for accurate calculations of forces and torques acting on the object.
Yes, the z component of the center of mass can be negative if the majority of the object's mass is located below the z-axis. This indicates that the center of mass is below the z-axis.
The shape of an object can greatly affect the z component of its center of mass. Objects with more mass located above the z-axis will have a higher z component, while objects with more mass located below the z-axis will have a lower z component.
There are several methods for finding the z component of the center of mass of a complex shape, including the use of integrals, the parallel axis theorem, and the center of mass formula. It is important to choose the appropriate method based on the complexity and symmetry of the object.
