Challenging 2D Motion Problem: Ring Sliding + Mass Swinging | JEE Physics & Olympiad

Motion in 2D where we have more degrees of freedom than just 1, poses challenges for students at the undergrad level. We at this channel are committed to bring sort of problems which are unique in some sense while help students learn concepts and methods for solving problems at IIT JEE or Olympiad level.

This problem is about a ring and a mass attached to it, where ring can slide on the smooth wire while the mass is free to swing or move in the 2D space. The motion is not simple and hence it makes it complicated for students to comprehend and solve these kinds of problems efficiently.

The problem description is as follows.

P1 and P2 have masses 3m and m, the rail is smooth, and the system moves under uniform gravity. Initially, the system is released from rest with the string making an angle θ0 (=π/3) with the downward vertical. Find the expression for velocity and angular velocity of the masses. What would be the velocity when the string becomes vertical?
Also, find the expression for time period of the full oscillation.


First get the logical understanding of the motion properly. Then draw the FBD. Then use the energy and linear momentum conservation to come up with the equations. And then solve for velocity and angular velocity of the masses.

Introduction: 0:06
Problem Statement: 0:27
FBD: 2:30
Conservation of Energy: 4:16
Linear momentum conservation: 7:00
Anagular velocity equation: 11:11
Velocity equation: 11:30
Velocity when masses are vertical: 12:40
Time period for full oscillation: 14:45

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