Disk A and B are identical and roll across a floor with equalspeeds. Then disk A

Question

Disk A and B are identical and roll across a floor with equalspeeds. Then disk A rolls up an incline, reaching a maximum heighth, and disk B moves upl an incline that is identical except that itis frictionless. Is the Maximum height reached by disk B greaterthan, less than, or equal to h?

I figured out that disk B would reach a lesser height than disk Adue to the fact that its deceleration is greater than disk A'sdeceleration. (Used Newton's second law)

How would I explain the difference in heights using conservation ofenergy? I keep thinking that disk B would not stop because it hasKE at the bottom - no friction - so it keeps going. But then wheredid the rotational energy go? What am I missing?

Explanation / Answer

firstly, the motion of each disk can be considered into 2components, linear motion ofthe center of mass , and the rotational motion. for disk B, frictionless , so the rotational motion energydoesn't affect to the height, which it gained., only linear motion,transfered to the potential energy Compared to the disk A, total energy (including linear androtation) transfer to the potential gravitation (or higher inheight). the result is disk A athigher position than B

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