No, the angular velocity of a body moving in a circle with a constant speed will not remain constant.
Angular velocity is defined as the rate of change of angular displacement over time. When an object moves in a circle at a constant speed, it experiences a continuous change in angular displacement as it moves around the circle. Therefore, its angular velocity is not constant.
The angular velocity of an object moving in a circle is given by the formula:
Angular velocity (ω) = Δθ / Δt
Where Δθ represents the change in angular displacement and Δt represents the corresponding change in time. As the object moves around the circle, Δθ increases with time, resulting in a changing angular velocity.
However, it's important to note that the linear velocity (tangential velocity) of the object remains constant if its speed remains constant. The linear velocity is the rate at which the object covers linear distance along the circumference of the circle.