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the fallowing question asks you to examine the motion of a hoola hoop traveling down an...

the fallowing question asks you to examine the motion of a hoola hoop traveling down an incline. The hoops center of mass is initially at some initial height zi and at the bottom of the ramp, the center of mass is zfoff the ground. The hoop has a radius R and mass m. The moment of inertia for a ring is I=mR2 The hoop travels down the hill without slipping. Consider the system being analyzed.

What is the work done by the friction on the hoopas it rolls down the hill. Justify your answer briefly. If friction does no work, what does it do tot he system? If it does do work, where does this work go?

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Answer #1

The dynamics of the rolling motion of the hoop rolling down a ramp can be analysed using the conservation of mechanical energy. And using the fact that the moment of inertia of the hoop is very high in comparison with other objects we can verify that the rotational kinetic energy of the hoop is maximum while it's translational kinetic energy is low. Now below I have used the conservation of energy to determine the expression for the acceleration of the hoop.

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