A thin spherical shell of radius R lying on a rough horizontal surface is hit sharply and horizontally by a cue. Where should it be hit so that the shell does not slip on the surface?
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The shell should hit at height h = 2R / 3
Explanation:
Let the cue strikes at as height h above the center for pure rolling
Vc = Rω
Applying law of conservation of angular momentum at point A.
Linear momentum imported to sphere = x
Vc = rωc
−μCh−θω=0
mvCh = 2 / 3 m R^2(Vo / R)
mvCh = 2 / 3mR^2(Vo / R)
h = 2R / 3
Thus the shell should hit at height h = 2R / 3
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