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Grade upto college level Mechanics

If the top of Fig. were not spinning, it would tip over. If its spin angular momentum is large compared to the change caused by the applied torque, the top precesses. What happens in between when the top spins slowly?
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

Profile image of Shane Macguire
11 Years agoGrade upto college level
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1 Answer

Profile image of Deepak Patra
11 Years ago
The angular speed of precession of spinning top is given as: 233-2414_1.PNG