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# Measuring the moment of inertia of a flywheel.

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Introduction

Title Measuring the moment of inertia of a flywheel. Objective Measure the angular velocity of a flywheel and use conservation of energy to calculate its moment of inertia. Apparatus Flywheel String Slotted mass on hanger Stop-watch Vernier caliper Metre ruler Theory The rotational kinetic energy can be defined by the equation K=1/2 I ?2. Where I is the moment of inertia of the body about the axis of rotation. In this experiment, the flywheel rotates freely about a horizontal axis. The radius of the axle of the flywheel can be measured with a caliper. As m falls, its gravitational potential energy is transferred into translational kinetic energy of m, rotational kinetic energy of the flywheel and work done by friction. As the flywheel completes N further turns, its original rotational kinetic energy is transferred into friction loss. Assume the flywheel decelerates uniformly. Thus, the moment of inertia of the flywheel can be determined. Procedure 1. The flywheel was set as shown with the axle of the flywheel horizontal. ...read more.

Middle

10. The mass was winded up again and steps 7 to 9 were repeated for at least 3 times. The mean values of the falling time t and n2 were obtained. Precautions 1. The mass and the height from which the mass falls should be chosen so that the falling time is long enough for measurement to be taken accurately. The mass and the height should not be changed throughout the experiment once they have been chosen. 2. The first few turns of the string should overlap the others. 3. The mass should be wound up to the same height in all trials. 4. When using the stop-watch, the hand should be held straightly to minimum the reaction time error. 5. Do not stand too close to the polystyrene tile when releasing the mass. 6. When choosing the appropriate amount of the slotted mass, a smaller amount (e.g. 1 slotted mass) should be chose to try first. 7. The later turns of the string should not overlap the others. ...read more.

Conclusion

Since the kinetic energy acquired by the flywheel ( 1/2 I?2) is dissipated in n2 revolutions, n2W = 1/2 I?2 W = I?2 / 2n2 Substituting, mgh = 1/2 mv2 + 1/2 I?2 + n1W mgh = 1/2 mv2 + 1/2 I?2 + n1I?2 / 2n2 I = mr2 ( n2 / n1 + n2 ) ( gt2 / 2h - 1) =0.2 � (0.0261)2 ( 25 / (25 + 5) ) ( 10 � (1.81)2 / 2 � 0.8 - 1 ) =2.21 � 10-3 kg m2 Conclusion The moment of inertia of the flywheel is measured and found to be 2.21 � 10-3 kg m2. Discussion Errors and improvement 1. The reaction times error. This can be improved by straighten the hand when taking the time. 2. The number of revolution n2 that the flywheel performed cannot be accurately obtained. This can be improved by counting the number of revolution by two students instant of one and to repeat the experiment more times. 3. Unsteady hands. When the hand released the mass, force may be push to the mass. To improve this, student should release the mass slowly and softly. Reference Physic Beyond 2000 ...read more.

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