A bead moves in a smooth radial groove of a horizontal disc rotating with constant angular speed ω. Which statements are correct?
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Question

A bead moves in a smooth radial groove of a horizontal disc rotating with constant angular speed ω. Which statements are correct?

G1 Physics · Accepted Answer

The radial equation is d²r/dt²=ω²r. The transverse acceleration is a_θ=2ω(dr/dt), so the groove reaction magnitude is 2mω|dr/dt|. Therefore, when dr/dt=0, the transverse acceleration and groove reaction are zero at that instant. The bead's kinetic energy need not be constant because the rotating constraint can transfer energy to the bead through the external mechanism maintaining constant ω.