A rod AB of mass m and length l can rotate about an axis passing through end A and perpendicular to the length of the rod. A bead of mass m can be slide along the length of the rod is initially at a radial distance $$l/3$$ from the axis of rotation. The rod starts rotating with angular velocity ω. Due to the action of centrifugal force, the bead starts sliding. What will be the angular velocity of the rod when the bead arrives at end B?

Question

A rod AB of mass m and length l can rotate about an axis passing through end A and perpendicular to the length of the rod. A bead of mass m can be slide along the length of the rod is initially at a radial distance $$l/3$$ from the axis of rotation. The rod starts rotating with angular velocity ω. Due to the action of centrifugal force, the bead starts sliding. What will be the angular velocity of the rod when the bead arrives at end B?

Infinity Learn · Accepted Answer

Conserving angular momentum,       $$13ml2+ml2$$ω'$$=13ml2+ml32$$ω⇒ω'$$=$$ω$$3$$

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