Is it possible for the angular momentum of an object to be zero if the angular velocity is nonzero? Is it possible for the angular velocity of an object to be zero if the angular momentum is nonzero? Explain.

Yes, it is possible for an object to have a zero angular momentum but a non-zero angular velocity. As an example, consider a massless object moving in a circular path. The change in angular displacement of object accounts for its non-zero angular velocity.However, being massless, the object has zero angular momentum.
It is important to note that the angular momentum of an object is given by the relation . However, the relation holds when the object is symmetrical about its axis of rotation. For asymmetrical objects, the relation does not hold. Therefore, one cannot use above relation to infer that an object with zero angular velocity will also have zero angular momentum or vice-versa.
An object with zero angular velocity is a non-rotating object. If the linear momentum of such an object is in the direction of the position vector of the object, the angular momentum of the object will also be zero. However, if the linear momentum of such an object is not in the direction of the position vector of object, the object will have a non-zero angular momentum.