A thin uniform rod of mass m and length l is hinged at the lower end to a level floor and stands vertically. It is now allowed to fall, then its upper end will strike the floor with the velocity

When a thin, uniform rod of mass m and length l , is hung at the lower end and allowed to fall vertically, it turns about this hinge. Gravity acting down on the thin rod has caused it to turn. Potential energy is transforming into kinetic energy.

Initially, when the rod is vertical, its center of mass is at a height of l/2 from the hinge. As it falls, this height has decreased. Right before the top end hits the floor, all the gravitational potential energy has been converted to kinetic energy, and velocity will have increased significantly at the top of the rod.

The velocity of the upper end of the rod upon striking the floor can be found by analyzing the motion and energy transformations involved. The distance between the center of mass and the upper end of the rod will play a crucial role in determining the final velocity when the rod is rotating. By the time the top end hits the ground, it has gained a particular velocity, which depends on the length of the rod and the effects of gravity. This is a great example of rotational dynamics and energy conservation in practice.