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12 Aug 2009 21:58:45 IST

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1.A uniform ring of mass m and radius r is given an angular speed w about the vertical axis passing

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1.A uniform ring of mass m and radius r is given an angular speed w about the vertical axis passing through its centre.If the ring is placed on a smooth horizontal surface .Find the tension in the ring. Also find the tension if a friction U(mew) exists between the ring and the surface???

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Soumen Goswami

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Joined: 10 Apr 2007

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12 Aug 2009 22:32:54 IST

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Let the tension in the ring be T. Consider a small element on the circumfurence of the ring making an angle at the centre. Make the free body diagram of this element. The tension forces are tangential to this element. You can easily check that the net inward force on the element is . Equate this to the centrepetal force on the element and you'll get T.

If there is friction, the tension won't be uniform on the ring. The increment in tension across an element will equal the frictional force. The procedure is similar to the first part.

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