E=U+KT (where KT is the translational kinetic energy and is equal to the familia

Question

E=U+KT (where KT is the translational kinetic energy and is equal to the familiar 12mv2), but E=U+KT+KR, where KR is the kinetic energy of rotation that the marble has when it's rolling.

Part A Given that the marble starts from rest, what is its initial mechanical energy, in terms of any non-zero quantities? Given that the marble starts from rest, what is its initial mechanical energy, in terms of any non-zero quantities?

E=U+KT+KR

E=0

E=U

E=U+KT

E=KT+KR

Part B The fact that the ball has some kinetic energy due to its rotation (KR) implies that The fact that the ball has some kinetic energy due to its rotation () implies that

K_T is the same as if the marble were not rolling

K_T must be smaller than what it would be if the marble were not rolling and had no rotational kinetic energy

K_T must be larger than what it would be if the marble were not rolling and had no rotational kinetic energy

Explanation / Answer

E must be equal to internal energy or U
Answer: E = U

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E=U+KT+KR
So, if Marble is roling, automatically, it will have higher KT
Answer: K_T must be larger than what it would be if the marble were not rolling and had no rotational kinetic energy

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