A wheel of mass $$5$$ kg and radius $$0.40$$ m is rolling on a road without sliding with angular velocity of $$10$$ rad $$s-1$$. The moment of inertia of the wheel about the axis of rotation is $$0.65$$ kg $$m2$$. The percentage of kinetic energy of rotation in the total kinetic energy of the wheel is

Question

A wheel of mass $$5$$ kg and radius $$0.40$$ m is rolling on a road without sliding with angular velocity of $$10$$ rad $$s-1$$. The moment of inertia of the wheel about the axis of rotation is $$0.65$$ kg $$m2$$. The percentage of kinetic energy of rotation in the total kinetic energy of the wheel is

Infinity Learn · Accepted Answer

Here, m $$=$$ $$5$$ kg, I $$=$$ $$0.65$$ kg $$m2$$          ω $$=$$ $$10$$ rad $$s-1$$,  R $$=$$ $$0.40$$ mLinear velocity        v $$=$$ Rω $$=$$ $$0.40$$× $$10$$ $$=$$ $$4$$ $$ms-1Translatiional$$ $$KE$$          $$=$$ $$12mv2$$ $$=$$ $$12$$×$$5$$×$$16$$ $$=$$ $$40$$ JRotational $$KE$$        $$=$$ $$12I$$ω$$2$$ $$=$$ $$12$$×$$0.65$$×$$100$$ $$=$$ $$32.5$$ JTotal $$KE$$ $$=$$ Translational $$KE$$ $$+$$ Rotational $$KE$$         $$=$$ $$40+32.5$$ $$=$$ $$72.5$$ JPercentage of rotational $$KE$$ $$=$$ Rotational KETotal $$KE$$  ×$$100$$                                             $$=$$ $$32.572.5$$×$$100$$ $$=$$ $$44.8$$%

A wheel of mass 5 kg and radius 0.40 m is rolling on a road without sliding with angular velocity of 10 rad s-1. The moment of inertia of the wheel about the axis of rotation is 0.65 kg m2. The percentage of kinetic energy of rotation in the total kinetic energy of the wheel is

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