Question

a particle is rotating about an axis in x-y plane then find out the turning moment of the particle about the axis of rotation

Answer 1

A particle is rotating about an axis in x-y plane.

Suppose, this axis has coordinates $x = x_0, y = y_0$ .

Then, its coordinates satisfy the equation:

$(x - x_0)^2 + (y - y_0)^2 = r^2$ - equation of circle

r - radius of rotating

turning moment (or torque) - is the tendency of a force to rotate an object about an axis, mathematically, torque is defined as the cross product of the lever-arm distance and force, which tends to produce rotation:

$\tau = r \times F$

or

$\tau = r * F * \sin(\theta)$

$\mathbf{F}$ is the force vector, and $\mathbf{F}$ is the magnitude of the force,

$\theta$ is the angle between the force vector and the lever arm vector.

$\pmb{\tau}$ is the turning moment vector and $\pmb{\tau}$ is the magnitude of the turning moment.

For, example, if F - force of tension of string and $\theta = 180$ , then $\tau = 0$ .