Total kinetic energy for a rigid object undergoing both translation and rotation (8-12)
Question
Total kinetic energy of a system that is both translating and rotating
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Review
We can also use the principle of conservation of energy for a rigid object that’s both moving through space as a whole and rotating. In such a situation it turns out that we can write the object’s total kinetic energy as the sum of two terms: the translational kinetic energy associated with the motion of the object’s center of mass (see Section 7-7), and the rotational kinetic energy associated with the object’s rotation around its center of mass (Figure 8-12). If the object has mass M and its center of mass is moving with speed vCM, its translational kinetic energy is K=12Mv2CM ; if the object’s moment of inertia for an axis through its center of mass is ICM and it rotates with angular speed ω, its rotational kinetic energy is Krotational=12ICMω2. The total kinetic energy (translational plus rotational) of the object is then:
