The following motion is based in the law of conservation of angular momentum

A) merry-go-round at a playground 

B) diving of diver

C) rotation of ballet dancer on smooth horizontal surface  

D) a solid sphere that rolls down on an inclined plane

A) merry-go-round at a playground 

B) diving of diver

C) rotation of ballet dancer on smooth horizontal surface  

In above three, examples the torque due to external force is zero.

A solid sphere that rolls down on an inclined plane. In this torque due to friction acts on the sphere. So, angular momentum is not conserved.