Irodov Problem 1.235

Physics · mechanics

Problem

A force F = Ai + Bj is applied to a point whose radius vector relative to the origin of coordinates 0 is equal to r = ai bj, where a, b, A, B are constants, and i, j are the unit vectors of 47 the x and y axes. Find the moment N and the arm 1 of the force F relative to the point 0.
Intuitive explanation

The moment of a force measures rotational effect around a point—it's the cross product of position and force vectors. Here, you'll compute N⃗=r⃗×F⃗\vec{N} = \vec{r} \times \vec{F} in 2D (which gives a scalar or zz-component), then find the perpendicular distance ll from the origin to the line of action using N=F⋅lN = F \cdot l. The key insight is that the moment arm is the shortest distance the force's line is from the pivot point, not the magnitude of r⃗\vec{r} itself.

Intuitive explanation

The moment of a force measures rotational effect around a point—it's the cross product of position and force vectors. Here, you'll compute N⃗=r⃗×F⃗\vec{N} = \vec{r} \times \vec{F} in 2D (which gives a scalar or zz-component), then find the perpendicular distance ll from the origin to the line of action using N=F⋅lN = F \cdot l. The key insight is that the moment arm is the shortest distance the force's line is from the pivot point, not the magnitude of r⃗\vec{r} itself.

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