A rigid horizontal smooth rod AB of mass 0.75 kg and length 40 cm can roate freely about a fixed vertical axis through its mid point O. Two rings each of mass 1 kg are initially at rest at a distance of 10 cm from O on either side of the rod. The rod is set in rotatiob with an angular velocity of 30 radians per second. Find the velocity of each ring along the length of the rod in m//s when they reach the ends of the rod. .

A rigid horizontal smooth rod AB of mass 0.75 kg and length 40 cm can

1.	A rigid horizontal smooth rod AB of mass 0.75 kg and length 40 cm can roate freely about a fixed vertical axis through its mid point O. Two rings each of mass 1 kg are initially at rest at a distance of 10 cm from O on either side of the rod. The rod is set in rotatiob with an angular velocity of 30 radians per second. Find the velocity of each ring along the length of the rod in m//s when they reach the ends of the rod. .
Answer» SOLUTION :From conservation of linear momentum `I_(1) omega_(1) = I_(2) omega_(2)` `((ml^(2))/(12) + 2ma^(2)) omega_(1) = [((ml^(2))/(12) + 2M((l)/(2))^(2))]omega_(2)` `omega_(2) = 10 rad//sec` form conservation of energy `(1)/(2) I_(1) omega_(1)^(2) = (1)/(2) I_(2) omega_(2)^(2) + 2 xx (1)/(2) MV^(2)` `v = 3 m//s`.