A ball rolls without slipping. The radius of gyrat
Question:
A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its center of mass is K. If radius of the ball be R, then the fraction of total energy associated with its rotational energy will be
In rolling without slipping, total energy of ball is the sum of its translational and rotational energy. Kinetic energy of rotation Krot=21Iω2=21MK2R2v2 where K is radius of gyration. Kinetic energy of translation, Ktrans=21Mv2 Thus, total energy E=Krot+Ktrans =21MK2R2V2+21Mv2 =21Mv2(R2K62+1) =21R2Mv2(K2+R2) Hence KtransKrot=21R2Mv2(K2+R2)21MK2R2v2 =K2+R2K2
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Top Questions on System of Particles & Rotational Motion
The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.