CROSS PRODUCT, 3D Sum of Moments Example in 90 Seconds!

About this video

• Video Title: CROSS PRODUCT, 3D Sum of Moments Example in 90 Seconds!
• Channel: Less Boring Lectures
• Speakers: Not specified
• Duration: 00:01:24

Overview

This video demonstrates how to calculate the moment of a force about a point in 3D space using the cross product. It provides a specific example, expressing the resultant moment as a Cartesian vector. This is presented as a third example within a larger series on rigid body equilibrium and moments.

Key takeaways

• The moment of a force is calculated as the cross product of the distance vector from the point of interest to the point where the force is applied, and the force vector itself.
• To find the moment, first determine the distance vector from point P to point A.
• The cross product can be calculated using the determinant of a 3x3 matrix, with orthogonal unit vectors in the first row, distance components in the second, and force components in the third.
• Evaluating this determinant yields the Cartesian components of the moment vector.
• The resulting moments for this specific example are 24 kNm (clockwise) for x, 24 kNm (counterclockwise) for y, and 8 kNm (counterclockwise) for z.