The hammer or discus moves in the direction it was moving at the time it was released.
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An athlete gives the hammer or discus a circular motion by rotating his/her own body before releasing it.
The athlete changes direction six times while running along a hexagonal track.
The stone’s tangential motion upon release indicates that the direction of motion was changing at every point while it was moving along the circular path.
The stone moves in a straight line when released because it continues to move in the direction it was moving at the instant of release, following the principle of inertia.