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Hooke had already deduced inverse-square gravitation from Kepler's third law, so he understood the second law. He just could not prove that the bound motion in response to an inverse square attraction is an ellipse. The source of Newton's second law was Galileo's experiments and thought experiments, especially the principle of Galilean relativity.
I reviewed Deriving F = ma - Newton's Second Law of Motion, but it just assumed F = Δp / Δt. Infinitesimal time form F = ma is derived from its discrete form F = Δp / Δt and not the other way round. It is axiomatically stated as a Law by Newton in the earliest times of calculus development defining infinitesimals of time and velocity .
Newton's law is valid when the 2nd term is negligible (approximately zero curvature). EDIT: A bit more detail. You correctly mention that Newton's law is valid in non-accelerated frames. The first term encompasses the accelerated motion (change in momentum) of the object in the frame. The second term accounts for the acceleration of the frame ...
Newton's I law: It defines what inertial frames are -- You can't prove a definition, you can only state a definition. Newton's II law: It is partly a definition, partly an empirical law. Newton's III law: It is an empirical law. Empirical laws can be seen as a general declare about our nature - something that can only be disproved by experiments.
Solution. Verified by Toppr. Newton’s second law of motion states that the force exerted by a body is directly proportional to the rate of change of its momentum. For a body of mass ‘m’, whose velocity changes from u to v in time t, when force ‘F’ is applied. F ∝ C h a n g e i n m o m e n t u m T i m e.
Newton’s Second Law of Motion states that force is equal to the change in momentum per change in time. For a constant mass, force equals mass times acceleration, i.e. F = m*a. Learn about the Acceleration in detail here. Newton’s Third Law of Motion states that for every action there is an equal and opposite reaction.
Now, when you say that Newton's second law is "not always perfect" due to factors like air resistance and friction, you are saying that you want to ignore other forces. The full statement of Newton's second law is $$\Sigma F = ma$$ where the sigma ($\Sigma$) means sum. So, if you add together all the forces on your object, you will get exactly ...
So one can encode these qualitative, but accurate, descriptions in a definition F = dt(mv ) F → = d t (m v →). So F F →, by definition, encodes the "strength" of the interaction that begets a change dt d t of state of motion mv m v →. The stronger the interaction, the swifter the deviation from the First-Law-foretold motion.
If there were an external force acting on the two objects, and they were our system, then we would use Newton's 2nd law to find the resulting motion of the center of mass of the system. Or we would use the force on each object to determine its individual motion. @d_b points out below that the law itself is for a single particle but by ...
$\begingroup$ @Nathaniel If jerk is bounded away from zero in the past then Newton's 2nd law is totally OK with jerk being continuous and the body moving on. But Newton's 1st law would insist that the jerk drop down discontinuously to 0 and the object remain at rest, merely because the position, velocity, and force all instantaneously were 0 ...
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