Physics

Physics

Problem

A force F⃗=5 i^+2 j^−4 k^ N\vec F = 5\,\hat i + 2\,\hat j - 4\,\hat k\,\text{N} acts at a point whose position vector with respect to the origin is r⃗=3 i^−j^+2 k^ m\vec r = 3\,\hat i - \hat j + 2\,\hat k\,\text{m}. Determine: a. (i) the torque τ⃗=r⃗×F⃗\vec \tau = \vec r \times \vec F about the origin in unit-vector form b. (ii) the magnitude of τ⃗\vec \tau
Intuitive explanation

The key here is understanding torque as a rotational effect — it measures how much a force tends to twist an object about a point. Torque is found using the cross product τ⃗=r⃗×F⃗\vec{\tau} = \vec{r} \times \vec{F}, which captures both the magnitude of the force and how far it acts from the pivot point, weighted by the angle between them. Set up the determinant carefully and compute each component to find the full 3D torque vector.

Intuitive explanation

The key here is understanding torque as a rotational effect — it measures how much a force tends to twist an object about a point. Torque is found using the cross product τ⃗=r⃗×F⃗\vec{\tau} = \vec{r} \times \vec{F}, which captures both the magnitude of the force and how far it acts from the pivot point, weighted by the angle between them. Set up the determinant carefully and compute each component to find the full 3D torque vector.

Browse the problem library