![]() And W f is the work done to overcome the torque of friction.Īccording to law of conservation of energy, Therefore, in the equation above n denoted the number of winding of the rope or the string. That friction will depend on the number of windings the rope had on the ring. Taking that into account, the equation for the work done will be,Īs the flywheel generates when the rope slid over the circular ring and generated friction. When the weight came down there was some friction produced by rotating the still flywheel, some work was done on it. Where v is the linear velocity of the weight coming down Moreover, when the flywheel gained kinetic energy the weight coming down also gained some kinetic energy which is expressed as, I is the moment of inertia and is the angular velocity of the flywheel. And the equation for the same loss can be written as,Īt the same time when the weight came down to a new height the flywheel and the axle rotated which increased the kinetic energy of the system. Subsequently, the mass will have a loss in its potential energy. Considering it in a dynamic situation when we roll the ring the weight will come down to a new height. Moreover, it is also determined by the expression,įor derivation let us initially discuss the diagram of a flywheel and consider a few parameters and annotations which are needed during the derivation.Ĭonsider a weight of mass m hanging on a thread rolled on a rolling ring. I is the flywheel’s moment of inertia, m is the mass of the ring, N determines the rotation of the flywheel, n determines the winding numbers, h is the weight assembly’s height, g is as we all know the gravity value i.e., (9.81 m/s) and r is the axle’s radius. Initially let us have a look at the formula for the moment of inertia of a flywheel. The moment of inertia of a flywheel is based on some assumptions we will determine in this article and by considering the same flywheel during the derivation. An interesting fact is that in 1802 a steam locomotive engine flywheel for distributing its single cylinder’s power. The MOI of the flywheel always remains constant but the kinetic energy remains dynamic because of the changing rotational speed of the flywheel. Overall, it is kinetic energy that is directly dependent on the moment of inertia of the and the speed’s square. Speaking in terms of its usage it is a mechanical device that saves the rotational energy by saving the angular momentum. ![]() The mass is carried by one end of a string that is lightly coiled all around the peg. Also on the shaft or the axle, there consists of a little peg. ![]() The shaft is supported by two permanent supports and is placed on rolling elements. The flywheel is made out of large circular ring wheels with a robust axle protruding along either end. ![]()
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