Topic 10 ( CENTROIDS and Inertia )

Question 1

Definition: The geometric center of a shape, representing the average position of all points in a plane figure.
Use: Purely geometric and independent of material or weight distribution.

Answer 1

Centroid

Question 2

Definition: The point where the total weight of a body is considered to act.
Use: Depends on the weight distribution and material properties of an object.

Answer 2

Center of Gravity

Question 3

Definition: A measure of an object’s resistance to bending or twisting, calculated using centroids and shape geometry.
Relevance: Crucial in structural and mechanical design, influencing beam deflection, rotational stability, and load analysis.

Answer 3

Moments of Inertia

Question 4

definition: The geometric center of a plane figure or solid body. It represents the average position of all points in the shape, independent of material or weight distribution.

Answer 4

Centroid

Question 5

Definition: The point in a body or system where the total weight is considered to act. It depends on the weight distribution and is affected by the material’s density.

Answer 5

Center of Gravity (CG)

Question 6

Definition: A method for calculating the centroid of a complex shape by dividing it into simpler shapes, determining their individual centroids, and combining them using area-weighted averages.

Answer 6

Composite Parts Method

Question 7

definition: A measure of an object’s resistance to bending or rotational motion, calculated based on the distribution of its area or mass relative to an axis.

Answer 7

Moment of Inertia

Question 8

Definition: In centroid calculations, areas representing voids or holes are treated as negative to account for their absence in the overall geometry.

Answer 8

Negative Areas

Question 9

Definition: The perpendicular distance from a point or axis to the line of action of a force or area.

Answer 9

Moment Arm

Question 10

Definition: A rule used to assign positive or negative signs to values (e.g., clockwise or counterclockwise moments) for consistent calculations.

Answer 10

Sign Convention

Question 11

Definition: A reference framework (e.g., Cartesian coordinates) used to define the positions of points in a plane or space, crucial for locating centroids.

Answer 11

Coordinate System

Question 12

Definition: Attributes of a shape (e.g., area, volume, length) used to determine its centroid without considering material or weight.

Answer 12

Geometric Properties