The speed of a cyclist on a circular track remains constant. This means that while the cyclist is continuously changing direction to stay on the circular path, the magnitude of their speed does not change.
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The motion of the hammer or discus once released is similar to the motion of the piece of stone; both move in the direction they were moving at the time of release.
Examples include the motion of the moon and the earth, a satellite in a circular orbit around the earth, and a cyclist on a circular track at constant speed.
The hammer or discus moves in the direction it was moving at the time it was released.
An athlete gives the hammer or discus a circular motion by rotating his/her own body before releasing it.