Explain how torque can be expressed as a vector product of two vectors. How is the direction of torque determined?

Torque can be represented as a vector product of two vectors: the position vector and the force vector. In this context, the torque vector represents the rotational effect of a force applied at a distance from an axis of rotation. The position vector points from the axis of rotation to the point where the force is applied, while the force vector indicates the direction and magnitude of the applied force.

With torque considered as a vector, both its magnitude and direction are thus reflected. This makes it clearer how a force affects any kind of rotational motion. The magnitude of torque has two factors: the distance from the pivot to the point at which a force is applied as well as the angle through which the force is applied.

The direction of a torque vector is found using the right-hand rule. According to this rule, if you curl the fingers of your right hand in the direction of the force vector while keeping your thumb extended along the position vector, your thumb will point in the direction of the torque vector. This direction indicates the axis of rotation and the sense of rotation that the force will induce on the object. Overall, expressing torque as a vector product simplifies the analysis of rotational dynamics in various physical systems.

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