Newton has stated the law in early days of physics when concepts and experiments were at very initial stages comparatively. Newton initiated physics as subject separating it from natural philosophy in 1686 in the Principia. In definition of third law Newton used terms action and reaction; and mutual interactions of bodies on each other. For practical demonstration of the law Newton himself used terms ‘push’ and ‘pull’; these are regarded as ‘force ’now in mathematical equations. The concepts of units and dimensions was developed by Fourier **[11,12] **in 1822. Newton did not give any mathematical equation for the law for demonstration.

The one body exerts force on the second body; the second body also exerts equal and opposite force on the first body.

Force exerted by body B (Reaction) in opposite direction = - Force exerted by body A (Action) (1)

Thus, statement of Newton’s third of motion has wide range of applications when one body exerts force on the other in different ways in various physical phenomena. For complete understanding of the law all applications must be quantitatively studied and eq.(1) must be scientifically verified experimentally; like other laws of science. The qualitative explanation is not sufficient for complete understanding of any law. * *

The law has many applications in the existing physics ( science) e.g.

backward movement of gun ( may be called as reaction) when bullet is fired (action),

rebounding of ball when it strikes the wall or floor

backward motion of boat in water when person jumps from it towards shore

book remains stationary on the floor or table ( weight of book is action , force exerted by floor is reaction)

launching of rocket, exhaust moves backward say action and rocket moves forward ( also see section about EM Drive where deviations from law are speculated),

a swimmer moves in forward direction ( reaction) when pushes water backward with arms (action )

forward movement of person (reaction) by pushing ground backward (action) etc.

All the examples or applications of Newton’s third law of motion need to be experimentally confirmed quantitatively.

**5.1 Quantitative discussion** **of** **free fall and rebounding of spherical ball**

This phenomenon (falling and rebounding bodies of different shapes) is not quantitatively studied in literature. It is very important to understand it experimentally taking all possible factors in account. Here we try to understand an example i.e. free fall of suitable rubber (plastic) ball on suitable floor and its rebounding quantitatively. Consider a rubber ball of uniform composition of mass 0.2 kg falls freely in vacuum. Let it falls freely from height of 1meter. The ball is attracted by gravitational force of earth i.e. weight (mg, 0.2 g or 1.96 newton), it is action. The time taken by body to fall through distance of 1m can be determined by equation S = ½ gt2 as 0.45s.

As the ball touches the floor, both interact with each other and reaction arises due to mutual simultaneous interactions of ball and floor; as stated in the third law. Thus, obeying third law of motion the ball rebounds in upward (opposite) direction. Newton’s third law of motion implies equal and opposite action and reaction, so spherical ball rebounds to height of 1meter, apparently under certain conditions. In such cases action and reaction are equal in magnitude but opposite in direction.

Obviously falling of ball due to gravity is action, and rebounding upward of ball after mutual simultaneous interactions of both (ball and floor) is reaction. To understand the law completely, action and reaction have to be quantitatively measured. The experimental confirmation of some other applications of Newton’s third law of motion is quite tedious and complicated process.

**5.2 Discussion on falling and rebounding bodies of different shapes e.g. semispherical, cone, flat, irregular or typical shape etc.**

Now a suitable body of rubber (plastic) of uniform composition of mass 0.2 kg may have different shapes e.g. spherical, semi-spherical, umbrella shaped, triangular, square, hexagonal, cone, long pipe, flat, irregular or any other typical shape are considered. etc. These bodies can be precisely fabricated. The composition and mass of these artefacts are precisely same as that of rubber (plastic) ball. Thus, inherent characteristics of bodies remain the same. The bodies are such that they are not deformed during interactions.

**In case of falling bodies, action (force, weight or mg) is independent of shape: **Let all bodies are dropped in vacuum like spherical ball in vacuum under exactly identical conditions (on the same floor) like sphere of same mass. The action is same. All the bodies are attracted by the gravitational force of earth with same force as mass of each body is same. Like spherical ball, the bodies of different shapes fall freely in vacuum as upthrust does not exist. Thus force (weight), mg or action in each case (like spherical ball) is the same (0.2g or 1.96 newton) for bodies of different shapes. Action (force or weight or mg) is independent of shape.

Now Newton’s Third law of motion as in eq.(1) implies that reaction is precisely equal and opposite to action for all pairs of bodies. In definition or equation of third law of motion there is no factor, that action and reaction may have different magnitudes. Newton’s third law does not put any constraint on reaction of body due to orientation (i.e. angle at which bodies are dropped.) Thus, as all bodies (of different shapes) would have same reaction (0.2g or 1.96 newtons) as action is the same (0.2g i.e. 1.96 newtons).

**Reaction must be precisely equal to action irrespective of other factors**. Thus, all bodies have same action i.e. force or weight (0.2g or 1.96 newtons) like spherical ball so all bodies should rebound to height of 1meter as reaction should be the same; according to Newton’s Third law of motion i.e. eq.(1). For example a spherical ball under some conditions rebounds to original height 1m . Thus law is obeyed , action = -reaction.

But the bodies of different shapes (as cited above), do not rebound to original height of 1 meter i.e. point they are dropped. It is observed even in daily life observations and is motivation for the quantitative experiments.

In some cases (flat or irregular shape body), may rebound to least height. Thus, reaction (force arises due to interaction of body and floor) appears to be less in body of different shapes; however, action for all bodies of different shapes is same as that of spherical body. Realistically action (force or weight) i.e. 0.2g or 1.96 newtons, is same for all bodies (different shapes) but reaction (force) is different as bodies rebound to lesser height. The distance can be calibrated in terms of reaction, as action is same for all bodies.

**Area of contact of falling or rebounding bodies with floor. **This aspect can be understood by fabricating bodies such as cone (pointed base), long pipe, typical body etc. such that area of contact of each body with floor is same as that of sphere.

Thus, even in case of different shapes, area of contact (projectile and target) can be same as that of spherical ball. The law is silent about symmetry of bodies if action is same then reaction has to be equal in magnitude and opposite in direction, according to law i.e. eq.(1). However, some bodies may not rebound precisely in opposite direction.

If the area of contact of body with floor is more then sound energy, heat energy (mass x specific heat x rise in temperature) need to be measured. It causes dissipation of fraction of energy. The rise in temperature of body when body falls on the floor is regarded as negligible. The temperature of target can be regarded as lower for observations. This aspect is required to be critically, specifically and quantitatively studied. It is not scientific to just understand the phenomena qualitatively.

**Qualitative Observations:** In qualitative observations the bodies rebound to different heights depending on its shape and size. Now with sensitive equipment, these experiments must be conducted to understand the phenomena quantitatively.

Newton’s law rigidly implies that action and reaction both must be equal; when body rebounds upward then acceleration due to gravity is regarded as -g as in projectile motion and other phenomena e.g. understand book rests on table. This aspect requires specific quantitative observations.

The vertical and horizontal distances travelled by bodies should be tabulated in repeated experiments using bodies of different shapes along with various trajectories while rebounding. In past 335 years this issue is not studied as there are no specific experimental data quantitively. Again, for understanding effect of shape, the mass and composition of bodies need to be precisely same.

In this case experimentally orientation (angle at which bodies fall) and symmetry (distribution of mass of body due to shape) appear to be equally significant factors; even if force of action is same (0.2g, 1.96 newtons) in all bodies. It is assumed that bodies are not deformed during interactions.

**Limitations of the law quoted in existing physics**. In applications of Newton’s third law of motion, some deviations under some conditions have been quoted in quantitative study of electric and magnetic forces **[4].** But the noble and new facts quoted above need to be conducted.

**5.3** **Composition of all bodies is precisely same.**

Here it must be noted that specifically bodies of precisely same composition (suitable rubber or plastic) but of different shapes are considered or fabricated. So, the results would test the dependence of shape of bodies on third law of motion, as composition hence inherent characteristics of bodies (projectile and target) are same. As the composition is same so that the other characteristics of body do not affect the results only shape is the significant factor in experiments. Purposely the mass of all bodies of different shapes (e.g. spherical, semi-spherical, umbrella shaped, triangular, square, hexagonal, cone, long pipe, flat, irregular or any other typical shape are considered.) is regarded as same for simplicity. Thus, anomalous results would be observed due to shape of bodies only. The other bodies having different characteristics can be chosen but it may be somewhat difficult to draw concrete conclusions. Taking bodies of similar composition, the effect of other factors is eliminated and only shape would be the significant factor.