SBT Rotation Q41 solution | Pure Rotation of Rod in a Cylinder | JEE / NEET

SBT Rotation Q41 solution | Pure Rotation of Rod in a Cylinder | JEE / NEET

In this video, we solve Question No. 41 from the SBT book (Rotational Motion).
The problem involves a uniform rod of mass 4 kg and length 4 m placed vertically inside a fixed smooth hollow cylinder of radius 4 m. The rod is released from rest, and we are asked to find its angular speed when it becomes horizontal.

We first analyze the motion and show that the rod performs pure rotation about the center of the cylinder, since at every instant, both ends of the rod remain in contact with the smooth inner surface, and their velocity directions are tangential. By drawing perpendiculars to the velocity vectors at both ends, we see they meet at the center O, proving pure rotation about that point.

Then, we apply the principle of energy conservation — the loss in potential energy of the rod equals its gain in rotational kinetic energy — to calculate the angular velocity (ω) when the rod becomes horizontal.

This question beautifully connects geometry of motion, rotation about a fixed axis, and energy conservation — a must-understand concept for rotational mechanics!

👉 Watch till the end to fully understand how the rod’s motion is analyzed and how ω is derived step by step.

#Physics #rotationalmotion #sbtsolutions #class12physics #sbtphysics #energyconservation #sbt #jeephysics #neetphysics #mechanics #physicsconcepts #angularvelocity #rotation