A spectacular manifestation of the conservation of angular momentum is offered by our earth. The earth rotates about an axis going from the south to the north pole. The main force acting on the earth is the force of gravity from the sun. Because this force acts on the center of mass of the earth it does produce any torque with respect to the axis of rotation and so the angular momentum cannot change. This is what gives us a day of constant length since prehistoric times. Not only that but the axis of rotation of earth is tilted with respect to the plane formed by the orbit of earth around the sun. This tilt is what causes the seasons to change through the year because when we are on one side of the sun the tilt causes the northern hemisphere to see the sun at closer to normal angle of incidence than when the earth is on the other side of the sun. The result is the difference in climate between summer and winter at a given geographical location. It is because the angular momentum associated with the earths almost circular trajectory about the sun is conserved that it takes exactly half a year each year to get from one side of the sun to the other. So you can thank conservation of angular momentum for the fact that summer follows winter with remarkable reliability every half year.