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Circular motion


King Thando Mathe

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A small bead of mass m is threaded on to a smoth circular wire of radius r and centre O fixed in the vertical plane.Bead is projected with speed u from its highest point, A, of the wire.Find the reaction on the bead due to the wire when at P,in terms of m,g,r,u and ₩;where ₩ is the acute angle AOP.

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Hint (hope I’m allowed to post one). Let the speed of the bead at the given position be [latex]v[/latex]. Then you can calculate [latex]v^2[/latex] in two ways:

  • Using energy considerations, you can express the kinetic energy [latex]\frac12mv^2[/latex] in terms of [latex]m,g,r,\omega,u[/latex].
  • The centripetal force [latex]\frac{mv^2}r[/latex] can be expressed in terms of [latex]m,g,r,\omega,R[/latex] where [latex]R[/latex] is the reaction of the wire on the bead.

These equations should allow you to eliminate [latex]v[/latex] and solve for [latex]R[/latex].

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