The torque τ⃗ on a body about a given point is found to be equal to 𝐀 ×𝐋 where A is constant vec

step 1 My question is a torque T on a body about a given point is found to be equal to E cross L. Where

The torque τ⃗ on a body about a given point is found to be...

The torque $\vec{\tau}$ on a body about a given point is found to be equal to $\overrightarrow{\mathbf{A}} \times \overrightarrow{\mathbf{L}}$ where $\overrightarrow{\mathrm{A}}$ is constant vector and $\overrightarrow{\mathbf{L}}$ is the angular momentum of the body about that point. From this it follows that : (a) $\frac{\overrightarrow{3}}{\text { "i }}$ is perpendicular to $\overrightarrow{\mathbf{L}}$ at all instant of time (b) the component of $\overrightarrow{\mathrm{L}}$ in the direction of $\overrightarrow{\mathrm{A}}$ does not change with time(c) the magnitude of $\overrightarrow{\mathbf{L}}$ does not change with time (d) all the above

The torque $\vec{\tau}$ on a body about a given point is found to be equal to $\overrightarrow{\mathbf{A}} \times \overrightarrow{\mathbf{L}}$ where $\overrightarrow{\mathrm{A}}$ is constant vector and $\overrightarrow{\mathbf{L}}$ is the angular momentum of the body about that point. From this it follows that :
(a) $\frac{\overrightarrow{3}}{\text { "i }}$ is perpendicular to $\overrightarrow{\mathbf{L}}$ at all instant of time
(b) the component of $\overrightarrow{\mathrm{L}}$ in the direction of $\overrightarrow{\mathrm{A}}$ does not change with time(c) the magnitude of $\overrightarrow{\mathbf{L}}$ does not change with time
(d) all the above

Key Concepts

Angular Momentum

Angular momentum quantifies the amount of rotation an object has, taking into account its mass distribution and rotational speed. It is a vector quantity defined as either the product of the moment of inertia and angular velocity for a rotating rigid body or as the cross product of the position vector and the linear momentum of a particle. Angular momentum is conserved in isolated systems where no external net torque is acting, making it crucial in analyzing rotational motion.

Vector Cross Product

The vector cross product is an operation between two vectors in three-dimensional space, resulting in a new vector that is perpendicular to the plane of the original vectors. Its magnitude equals the product of the magnitudes of the two vectors and the sine of the angle between them. This property plays a key role in physics, especially in defining rotational quantities like torque and angular momentum, and in understanding how directional components of these quantities interact.

Torque

Torque is a measure of the tendency of a force to rotate an object about an axis. It is defined as the cross product of the position vector (relative to a point or axis) and the force vector, meaning that its direction is perpendicular to the plane formed by these two vectors. The concept of torque is fundamental in understanding rotational dynamics, where the influence of applied forces on the rotational state of an object is assessed.

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