# Conservation of mechanical energy applied on rolling

I have 2 questions

1. A small solid sphere with a translation velocity $$v$$ m/s is climbing up an inclined surface of height $$h$$. what is the minimum $$v$$ required to climb this height

This question is solved by applying conservation of mechanical energy on translational motion of ball

1. A disc of mass $$M$$ and radius $$R$$ rolls up on an inclined plane to a height $$h$$. if velocity of disc is $$v$$, the maximum height that the disc can reach is?

This question is solved by applying conservation of mechanical energy on both rotational and translational motion of disc

My problem is, how can we decide to apply conservation of mechanical energy on one component of kinetic energy or both?

• If rotation is involved and is changing then you must use both Commented Sep 23, 2021 at 8:37
• thank you! altho, in the first question only translational energy is converted to potential but in the second question both transational and kinetic energies are converted to potential. i dont understand how. changing rotation happens when? pls help Commented Sep 23, 2021 at 8:48
• If that's true then in question one the rotation doesn't change. Maybe the surface is slippery or something like that. Of the rotation did change, then some energy went to or from the rotational kinetic energy in which case it must be included in the calculations. In general, everything that changes ought to be included in the calculations. Commented Sep 23, 2021 at 9:05