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 continuously as the body moves along the circular path.
The linear velocity of an object moving in a circular path is defined as the rate at which the object's position changes with respect to time. It is the speed of the object in a specific direction tangent to the circle at any given point.
When an object is moving in a circular path with a constant angular velocity (constant rate of rotation), it means that the object is covering equal angles in equal time intervals. However, since the object is moving in a circular path, its linear displacement is not constant. As a result, the linear velocity of the object is not constant either.
The relationship between linear velocity (v) and angular velocity (ω) can be described using the formula:
v = ω * r
where: v is the linear velocity, ω is the angular velocity, and r is the radius of the circular path.
From this formula, we can see that the linear velocity is directly proportional to the angular velocity and the radius. Therefore, if the angular velocity remains constant, the linear velocity can still change if the radius changes. This means that the object can speed up or slow down as it moves along the circular path, depending on the radius of the path.