If a force, having a magnitude of 498 newtons, is eight centimeters away from point 𝐴, find the norm of the moment of the force about the point 𝐴, giving your answer in newton meters.
We’ll call our force magnitude, 498 newtons, capital 𝐹. And the distance from point 𝐴 at which the force acts, eight centimeters, we’ll call 𝑑. We want to solve for the norm of the moment of the force about point 𝐴. We’ll call that moment 𝑀.
In general, if we have a force vector 𝑭 acting at a point separated from the point 𝐴 by a vector 𝒓, then the moment 𝑴 of that force 𝑭 around point 𝐴 is equal to 𝒓 cross 𝑭.
In our case, because we’re solving for the norm of that moment, we can write a simplified version of the expression: 𝑀 is equal to 𝑑 times 𝐹. Both 𝑑 and 𝐹 are given in our problem statement. So we’re ready to plug in and solve for 𝑀.
When we do, we convert our distance into units of meters to be consistent with the required units of 𝑀. This product is equal to 39.84 newton meters. That’s the norm of the moment of the force about the point 𝐴.