Are there any situations in which we cannot apply Newton’s laws of motion? Is there any alternative for it?

1. Limitation : Newton’s laws of motion cannot be applied for objects moving in non-inertial (accelerated) frame of reference.

Alternative solution : For non-inertial (accelerated) frame of reference, pseudo force needs to be considered along with all the other forces.

2. Limitation : Newton’s laws of motion are applicable to point objects and rigid bodies. Alternative solution: Body needs to be approximated as a particle as the laws can be applied to individual particles in a rigid body and then summed up over the body. 

3. Limitation : Newton’s laws of motion cannot be applied for objects moving with speeds comparable to that of light. Alternative solution: Einstein’s special theory of relativity has to be used. 

4. Limitation : Newton’s laws of motion cannot be applied for studying the behaviour and interactions of objects having atomic or molecular sizes.

Alternative solution: Quantum mechanics has to be used.