A disk an a sphere roll off two inclined planes of the same altitude and length. Which of the two objects will get to the bottom of the respective plane first? how does the result depend on the masses and diameters of the disk and the sphere?
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1 Answers
39Age old question.
Acceleration(rolling without slipping) = (mgsin@)/(m + I/R2)
I = moment of inertia of body and R = radius of body.
For a disk, this becomes a = (2/3)gsin@
For a solid sphere, this becomes a = (5/7)gsin@
Obviously the solid sphere comes down faster.