Rolling ball

Conservation of Energy

(KEregular + KErotational + PEgravity)initial =

(KEregular + KErotational + PEgravity)initial + Elost

0 + 0 + mgh = (1/2)mv2 + (1/2)Iw2 + 0 + 0.

Substituting I=(2/5)mr2 and w=v/r gives:

mgh = (1/2)mv2 + (1/2)[(2/5)mr2][v2/r2] , or

mgh = (1/2)mv2 + (1/5)mv2 = (7/10)mv2 .

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