The particles have equal mass \( m \). In a 1D elastic collision, they exchange velocities.
Particle \( A_{bottom} \) (initially \( +u \)) acquires velocity \( -u \).
Particle \( B_{top} \) (initially \( -u \)) acquires velocity \( +u \).
The non-colliding particles retain their original velocities.

Velocities of particles in Dumbbell A:
Top: \( v_1 = +u \)
Bottom: \( v_2 = -u \)
Velocity of CM: \( v_{cm} = \frac{v_1 + v_2}{2} = 0 \). The dumbbell stops translating.
Angular Velocity: The relative velocity between ends is \( 2u \). \[ \omega = \frac{v_{rel}}{l} = \frac{2u}{l} \]