Final answer:
To calculate the moment of force about a point, use the cross product formula τ = r × F. The moment is expressed as a Cartesian vector, with its magnitude and direction determined by the position vector and the force vector.
Step-by-step explanation:
The moment of a force (also known as torque) about a point is calculated using the cross product of the position vector (from the point to where the force is applied) and the force vector. The formula is τ = r × F, where τ is the moment about the point, r is the position vector, and F is the force vector. To express the moment as a Cartesian vector, it is essential to know the perpendicular distance from point O to the line of action of the force F and the direction in which the force is applied.
For a force of 220 lb applied at a distance, first, find the perpendicular distance following the right-hand rule to determine the direction of the torque vector. For a given example, with a force acting at a position with specific x, y, z coordinates from the point of rotation, you would calculate the torque vector components using the determinants of a matrix composed of i, j, k unit vectors, the x, y, z coordinates of the position vector, and the x, y, z components of the force vector.