On a horizontal smooth plane there is a motionless vertical cylinder and disc A. A is connected to cylinder by thread AB. The disc is set in motion with initial velocity V. as shown. Then the angular momentum of the body is 

Top view of cylinder is given

weight is balanced by Normal reaction

resultant force= tension is initially acting at B

tension  changes as it rotates

torque about point O  is not zero.

 $\tau =TR in anticlockwise direction$

therefore L of particle about O  is not conserved

velocity of particle changes continuously as direction changes.

But KE remains constant as magnitude of velocity is constant