I have been doing personal study in Classical Mechanics and reading Newton's Laws. While thinking about them I had a question I haven't been able to answer. It comes from the interactions of Newton's 1st and 3rd laws. First law  In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.  Third law  When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.  So here's the problem: An object is in a certain state (at rest or in motion with zero acceleration) and an external force is applied to that object. By the 1st Law the object should experience a change of state. But then by the 3rd Law a reactive force, of equal magnitude and opposite direction, would be applied on the object and now the sum of the forces would be zero (the object's state doesn't change at all). By this reasoning it would be impossible for an object to experience a state change because these forces would be in constant opposition. But objects do experience state changes so where is the mistake in this reasoning? Thank you for any help!
4352
Given Newton's third law, why is there motion at all? Should not all forces even themselves out, so nothing moves at all? When I push a table using my finger, the table applies the same force onto my finger like my finger does on the table just with an opposing direction, nothing happens except that I feel the opposing force. But why can I push a box on a table by applying force ($F=ma$) on one side, obviously outbalancing the force the box has on my finger and at the same time outbalancing the friction the box has on the table? I obviously have the greater mass and acceleration as for example the matchbox on the table and thusly I can move it, but shouldn't the third law prevent that from even happening? Shouldn't the matchbox just accommodate to said force and applying the same force to me in opposing direction?
95828
I know this has been asked around, my question is a bit more specialized towards my personal problem.  If I have an object the magnitude of the weight is usually equal to the normal force, right?   I could be mistaken but from what I have read the normal force is the force the object is feeling opposite to the $(mass*gravity)$. If that is the case, and I put my hand on the object does my Force get added to the object's weight and thus the normal force of that object increases? Therefore if I keep adding hands to the object will the normal force keep compensating?   Also is the normal force the negative charged electrons repelling each other (electromagnetism)?
51933
The definition of  is  "Inertia is the resistance offered by the body whenever its state of motion is changed."   What is inertia of a body? Is inertia actually a force exerted by the body?  If so, then why is there no application of inertia in numerical problems involving application of force on a body? What is the actual application of inertia in theory?
3850
When a person lifts a book while standing on the earth's surface. Why is his force considered external to the book-earth system? Isn't his force internal like the case of the forces that cause the exploson of a bomb. I think the forces the person exerts on both the book and the earth are internal since they are equal but opposite therefore resulting in the position of the centre of mass of the system being maintained and if i'm right is the mechanical energy of the system constant?  Am i wrong? Please correct me.
25566
Newton's second law says $F=ma$. Now if we put $F=0$ we get $a=0$ which is Newton's first law. So why do we need Newton's first law ?   Before asking I did some searching and I got this: Newtons first law is necessary to define inertial reference frame on which the second law can be applied.  But why can't we just use Newton's second law to define an inertial frame? So if $F=0$ but $a$ is not equal to 0 (or vice versa), the frame is non-inertial.  One can say (can one?) we cannot apply the second law to define a reference frame because it is only applicable to inertial frames. Thus unless we know in advance that a frame is inertial, we can't apply the second law.  But then why this is not the problem for the first law?  We don't need to know it in advance about the frame of reference to apply the first law. Because we take the first law as definition of an inertial reference frame.  Similarly if we take the second law as the definition of an inertial frame, it should not be necessary to know whether the frame is inertial or not to apply the second law (to check that the frame is inertial).
116246
So this is the question that's been bothering me:  Say you have a simple rigid body in space that is at rest or traveling with only translational motion at a constant speed. Say that the body is something like a rod and it's not rotating. So, at some point, an external force is acted on the rod, just for an instant and it is not acted along some axis that goes through the center of mass. What will happen??  My guess is that it will start rotating about the center of mass (because of torque) + it will get some translational motion towards the direction of the force. Is that correct? and if so, how much of the force becomes rotation and how much translational movement and why??  Please forgive my English and thnx in advance!!
62225
On , it is written that      So, we see things falling with an acceleration which we call the acceleration of gravity,and thinking that we live in a straight line , uniformly moving or stationary inertial frame, we attribute that acceleration to a force, the force of gravity. Whereas in reality,objects falling towards the Earth are moving along geodesic paths with no acceleration and according to modified version of law of inertia, have no force acting on them. They fall simply because the curved space-time near the Earth ...   Now, why do the objects falling towards the Earth move along the geodesic paths with no acceleration? That means the objects don't have any force acting on them, but why? A body in a free-fall moves with acceleration $g$, so, why is it written like that? Why does the author use Law of inertia on freely falling body?? Law of Inertia can only be applied when no external force acts on the body. So, is the freely-falling body accelerates under force of gravity or moves uniformly while moving through geodesic paths as quoted by the author?
60355
"We have focused our discussion on one-dimensional motion. It is natural to assume that for three-dimensional motion, force, like acceleration, behaves like a vector."- (Introduction to Mechanics) Kleppner and Kolenkow  We learn it very early in the course of our study that Force is vector; But, if I were the physicist defining the the Newton's second law (experimentally) and analysing the result F=ma, how would I determine whether Force is vector or scalar(especially in 3-D).   Actually, when I read the aforementioned sentences from the book, I wanted to  know why do the authors expect it to be natural for us to think that in 3-D "Force" behaves like a vector. I know a(acceleration ) is vector and mass a scalar and scalar times vector gives a new vector but is there another explanation for this?
10731
I have asked a question on I  pushing the wall,where the force of me is not zero but as per the formula F=m.a,the force is zero and then I got the answer , it is because here the net force is acting on the body.But I a doubt that then a body of mass 5kg and moving with an acceleration 2m/s^2 will experience a force = 10N,Is in this case also the net force acting? Or  the net force is acting only when the body doesn't move? If this is correct then my question why?
57608
Newtons three laws of motion appears to apply only for linear motion:   An object remains at rest or moves in a straight line at uniform velocity unless a force is applied.  Force is mass times acceleration.  Every action causes an equal and opposite reaction.    Is there a rotational equivalence? For example:  1'. Every body rotates around a fixed axis at uniform angular velocity unless a torque is applied 2'. Torque is Moment of Inertia times angular acceleration 3'. When one body exerts a torque on another; there is an equal and opposite torque applied on the first body by the second.  First are these actually correct; if not, what are the correct equivalence; and who formulated them?
64188
A while back in my Dynamics &amp; Relativity lectures my lecturer mentioned that an object need not be accelerating relative to anything - he said it makes sense for an object to just be accelerating. Now, to me (and to my supervisor for this course), this sounds a little weird. An object's velocity is relative to the frame you're observing it in/from (right?), so where does this 'relativeness' go when we differentiate?   I am pretty sure that I'm just confused here or that I've somehow misheard/misunderstood the lecturer, so can someone please explain this to me.
98902
In whichever angle an object is thrown at a surface, the surface always exert force normal to it. But why? According to Newton's third law, if an object hits a surface at an angle, the reaction force provided by the surface must be equal and opposite to the applied force by the object. But why  does the surface always exert force normal to it?
112045
When a body lies on the surface of the Earth it is under the influence of gravity. The force on the body due to gravity causes it to exert a force on the ground and the normal reaction acts in the opposite direction causing the resultant force on the body to be zero.  However, how can the body exert a force on the ground when it does not have any acceleration? Since force equals mass times acceleration how does a body without acceleration experience a force?
8542
In (non-relativistic) classical physics, if the temperature of an object is proportional to the average kinetic energy ${1 \over 2} m\overline {v^{2}}$of its particles (or molecules), then shouldn't that temperature depend on the frame of reference - since $\overline {v^{2}}$ will be different in different frames?  (I.e. In the lab frame  $K_l = {1 \over 2} m\overline {v^{2}} $, but in a frame moving with velocity $u$ relative to the lab frame, $K_u =  {1 \over 2} m \overline {(v+u)^{2}}$).
76977
I was trying to think but cannot figure it out. For instance, if the interaction is small, for instance limited to a windows, the observers in each universe will see that the other goes in reverse. But what if they can start a more meaningful interaction? (for instance, if one observer crosses the window and moves to the other universe, will anything change? why and how fast? (at least at the beginning his thinking will move in the same time arrow than in his universe, but the physical processes around him will still violate the second law?
3173
Clearly, the Earth is accelerating (as it has centripetal acceleration), and thus it is a non-inertial frame of reference. Then, why don't we use pseudo forces all the time? My teachers told me that the effect produced by the centripetal acceleration of the Earth on our calculations is negligible and hence we can safely neglect pseudo force. But how? I want rigorous proof with examples that show exactly how much we are compensating in exchange for neglecting that the Earth is a non-inertial frame of reference.
45040
According to Newton's third law of motion, for every action there an equal and opposite reaction.  If an object A applies a force (action) on an object B, object B applies an equal and opposite force (reaction) on object A. If we consider this reaction force as the action force applied by object B on object A, shouldn't there be a reaction force for every reaction force and hence infinite reaction forces?