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| Motion in a Vertical Circle |
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| Consider a body of mass 'm' tied to a string and rotated in a vertical circle of radius 'r'. The velocity (speed) of the body keeps changing. It is maximum at the bottom and a minimum at the top. |
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| Let u be the speed of the particle at the bottom |
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| Let v be the speed at some point |
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| By the principle of conservation of energy |
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 Where (h is the vertical height of P above the lowest point) |
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| Let T be the tension in the string. |
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| Minimum velocity required at the bottom for looping the loop |
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| Tension at the highest point is obtained by putting h = 2r in |
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| Tension at the bottom of the circle is obtained by putting h = 0. |
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| Tension at the highest point is given by putting h=2r |
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 TL - TH = 6mg |
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