A

Step 1: Understand the terms involved in circular motion. A body moving in a circular path with uniform angular velocity experiences a change in direction continuously, which implies it is accelerating.
Step 2: Analyze the concepts:
- **Acceleration**: In circular motion, even if the speed (magnitude of the velocity) is constant, the direction is changing, resulting in centripetal acceleration directed towards the center of the circle.
- **Velocity**: Velocity has both magnitude and direction; here, the direction changes constantly, so it is not constant.
- **Momentum**: Similar to velocity, momentum (mass times velocity) also depends on the direction; thus, as direction changes, momentum is also not constant.
- **Kinetic Energy**: Kinetic energy depends solely on speed, which remains constant if the speed is uniform. However, it's not considered constant motion-wise as the direction changes.
Therefore, the correct answer is that the motion of the body has constant acceleration.