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

Question

G1 Physics · Accepted Answer

There is no external torque about O, so angular momentum is conserved while the rings slide. Initially initial I=I of rod+2m(0.10)² and initial ω=30 rad/s. At the ends, r=0.20 m, so final I=I of rod+2m(0.20)². Use initial Iinitial ω=final Ifinal ω, then conserve mechanical energy because the rod is smooth: ½initial Iinitial ω²=½final Ifinal ω²+2(½mradial speed²). Solving gives radial speed=3 m/s for each ring.