The law of conservation of energy explains that energy never is created nor destroyed. It only changes from one form to other form of energy. The law of conservation of energy is used when there is no non-conservative force on the system. Non-conservative force is dispersing forces like friction or air resistance, which take away energy from the system.

The law of conservation of linear momentum explains that the momentum of the system is conserved when there is no external force is applied to the system. This law of conservation of linear momentum is applicable when there is only internal force which does not affect the system.

The law of conservation of angular momentum explains that the angular momentum of the system is conserved when the external torque is not applied to the system. This law of conservation of angular momentum is applicable when there is no external torque on the system.

Conclusion:

Therefore, the law of conservation of energy is used when there is no non-conservative force on the system, the law of conservation of linear momentum is used when there is only internal force which does not affect the system and the law of conservation of angular momentum is used when there is no external torque on the system.