A ring of mass M and radius R is rotating with angular velocity w about central axis
Lying flat on a smooth horizontal surface. The tension developed in
the ring is
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Mw²R/2π
Method 1
You can assume a small portion of the rotating ring and evaluate the forces for force angular acceleration equation
Method 2
You can assume a half ring and evaluate the force angular acceleration equation on the centre of mass of the half ring
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Given a ring with mass 'M' and radius 'R.'
The ring has an angular velocity = ω rad/s
Let the tension in the ring be = T Newton
Let us assume a small portion AB on the ring.
The net force on the section AB is 2Tsin
The net force would be directed towards center C.
2Tsin = 2T (As the angle is small)
The mass of the portion AB is =
For the circular portion,
Thus, the tension appearing in the ring is Mω²R.
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