No, the linear velocity of a body does not remain constant when the body is moving on a circular path with a constant angular velocity. The linear velocity changes as the body moves along the circular path.
Linear velocity refers to the rate at which an object changes its position in a straight line. On the other hand, angular velocity refers to the rate at which an object rotates or changes its angular position. These two velocities are related but not the same.
When an object moves on a circular path with a constant angular velocity, it means that the object is rotating at a constant rate. However, because the object is moving in a curved path, its linear velocity is constantly changing.
To understand this, consider a point on the edge of a rotating object. As the object rotates, this point travels a certain distance in a given time, which is the linear velocity. Since the point moves along a curved path, its direction changes continuously, and hence, its velocity vector changes as well.
The relationship between linear velocity (v), angular velocity (ω), and the radius of the circular path (r) is given by the equation:
v = ω * r
This equation shows that the linear velocity depends on both the angular velocity and the radius of the circular path. As the object moves along the circular path, the radius remains constant, but the angular velocity remains constant. Therefore, the linear velocity of the body changes since it is directly proportional to the angular velocity.