Problem 1 A drum majors baton consists of two masses m1 and

Problem 1. A drum major’s baton consists of two masses m1 and m2 separated by a thin rod of length l. The baton is thrown up in the air with some velocity ~v at an arbitrary angle. Find the position of the center of mass of the baton (with respect to the masses) and describe its motion (neglect any air resistance).

Solution

let us take take m1 as origin

then coordinate of m2 = (l ,0)

centre of mass , COM = (m1 * 0 + m2* l ) / ( m1 + m2)

therefore position of centre of mass is at a distance m2* l/(m1+m2) from m1

the motion of the centre of mass is a projectile