The helicopter experienced a hard landing during a practice autorotation maneuver. In a written statement, the certificated flight instructor (CFI) reported that the purpose of the flight was to provide the private pilot training toward receiving his commercial license. The private pilot made several approaches to the active runway including straight-in autorotation maneuvers. Following an unsuccessful attempt at a 180-degree autorotation, the CFI instructed the private pilot to perform the maneuver again. The private pilot entered the autorotation with the helicopter configured at an airspeed of 75 knots. As the descent proceeded, the private pilot utilized the collective to maintain the rotor revolutions per minute (rpm) within the normal operating range. Through the turn, the CFI noticed that the helicopter was gradually assuming a nose-low attitude, with the airspeed increasing past 70 knots. The CFI advised the student to level the helicopter and continue to maneuver through the turn. As the helicopter descended through 300 feet above ground level (agl), the airframe began to vibrate and develop a high sink rate. The CFI assumed authority of the flight controls and the helicopter continued to descend through 100 feet agl. Configured at an airspeed of 40 knots, with a continuous vibration, the low-rotor rpm warning began to sound. The CFI leveled the helicopter while it simultaneously contacted the ground. The helicopter touched down hard and slid on its belly to the edge of the runway surface. The CFI reported no mechanical malfunctions or failures with the airframe or engine prior to the accident. He further stated that the accident may have been prevented if he had assumed authority of the controls earlier in the maneuver.