A drum major's baton consists of two masses `m_(1)` and `m_(2)` separated by a thin rod length l. The baton is thrown into the air. The problem is to find the baton's center of mass and the equation of motion for the center of mass.

A uniform rod of mass M and length L lies on a frictionless horizontal plane. A particle of same mass M moving with speed v_(0) perpendicular to the length of the rod strikes the end of the rod and sticks to it. Find the velocity of the center of mass and the angular velocity about the center of mass of (rod + particle) system.

Two uniform thin rods each of length L and mass m are joined as shown in the figure. Find the distance of centre of mass the system from point O

Two uniform thin rods each of length L and mass m are joined as shown in the figure. Find the distance of centre of mass the system from point O

Two uniform thin rods each of length L and mass m are joined as shown in the figure. Find the distance of centre of mass the system from point O

A thin rod of length L is bent to form a semi circle. The mass of the rod is M . What will be the gravitational potential at the centre of the circle?

Moment of inertia of a thin uniform rod about an axis passing through the center of mass and perpendicular to the length is

The velocities of two particles of masses m_(1) and m_(2) relative to an observer in an inertial frame are v_(1) and v_(2) . Determine the velocity of the center of mass relative to the observer and the velocity of each particle relative to the center of mass.

The linear density of a thin rod of length 1m lies as lambda = (1+2x) , where x is the distance from its one end. Find the distance of its center of mass from this end.