The radius vector and linear momentum are respectively given...

The radius vector and linear momentum are respectively given by vectors $2 \hat{i}+\hat{j}+\hat{k}$ and $2 \hat{i}-3 \hat{j}+\hat{k}$. Then the angular momentum is:
(a) $2 i-4 \hat{k}$
(b) $4 \hat{i}-8 \hat{k}$
(c) $2 \hat{i}-4 \hat{j}+2 k$
(d) $4 i-8 j$

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Key Concepts

Linear Momentum

Linear momentum is a vector quantity defined as the product of a particle’s mass and its velocity. It measures the quantity of motion and, when used with the position vector, contributes to the calculation of angular momentum, offering insights into the rotational aspects of a system.

Position (Radius) Vector

The position or radius vector indicates the location of a particle relative to a chosen origin. In mechanics, this vector is used to describe spatial coordinates and, when combined with momentum, is essential for determining the angular momentum of a particle.

Cross Product

The cross product is an operation on two vectors in three-dimensional space that results in a third vector perpendicular to the plane formed by the original vectors. This operation is used to calculate angular momentum and incorporates both the magnitudes of the vectors and the sine of the angle between them, as well as the right-hand rule to determine direction.

Angular Momentum

Angular momentum is defined as the cross product of the position (or radius) vector and the linear momentum vector. It is a vector quantity that represents the rotational state of a particle or system and plays a key role in dynamics, especially in conservation laws related to rotational motion.

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