Explanation:

When a particle is moving in a circular motion, it experiences a change in direction at every point along its path. This change in direction is due to the centripetal force acting on the particle, which always points towards the center of the circular path. The linear velocity of the particle is defined as the rate of change of displacement with respect to time, and it is always tangential to the circular path.

Linear Velocity:
The linear velocity of a particle at any point on the circular path is directed along the tangent to the path at that point. This means that the linear velocity is perpendicular to the radius of the circle at that point, and it points in the direction in which the particle is moving.

Tangential Direction:
The tangent to a circle at any point is a straight line that touches the circle at only one point, without intersecting it. It represents the instantaneous direction of motion of the particle at that point. As the particle moves along the circular path, its direction of motion changes, and therefore, the tangent to the circle also changes.

Centripetal Force:
The centripetal force is responsible for keeping the particle moving in a circular path. It acts along the radius towards the center of the circle. This force provides the necessary inward acceleration for the particle to continuously change its direction and move in a circular path. The magnitude of the centripetal force is given by the equation:

F = (mv^2) / r

where F is the centripetal force, m is the mass of the particle, v is the linear velocity, and r is the radius of the circular path.

In conclusion, the linear velocity of a particle rotating in a circular motion is always directed along the tangent to the circular path at any given point. This is because the particle experiences a continuous change in direction, and the tangent represents the instantaneous direction of motion at that point.