# Conservation of mechanical energy

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1. Jan 24, 2015

"When a body (sphere) rolls in an inclined plane where half of the incline descends and has friction while the next half ascends and is frictionless, then mechanical energy is conserved in the part of incline having friction and only rotational energy is conserved in the part of incline lacking friction. Hence once the body starts ascending, only its translational energy is converted to potential energy" -- from book

I understood that you can conserve energy when friction is present because the friction does no work as point of contact of sphere is at rest (pure rolling). Hence the initial potential energy gets converted to kinetic energy (rotation+translation)

But why is it that the rotational energy is constant for the ascending part?

2. Jan 24, 2015

### Stephen Tashi

On the frictionless part of the plane, the sphere continues rotating. It has no traction so it's rate of rotation doesn't contribute to the linear motion of the center of the ball and the rate of rotation doesn't slow down.