2. Formula: F =ma
Newton's original formula: f = δ (MV)/δ t (see Newton's Mathematical Principles of Natural Philosophy). That is, the acting force is directly proportional to the rate of change of the momentum of the object, also known as the momentum theorem. In the theory of relativity, F=ma does not hold, because the mass changes with the speed, and f = δ (MV)/δ t is still used.
3. Some notes:
(1) Newton's second law is the instantaneous law of force. Force and acceleration occur at the same time, change at the same time, and disappear at the same time.
(2)F=ma is a vector equation, and the positive direction should be specified when it is applied. Any force or acceleration in the same direction as the positive direction should be positive, otherwise it should be negative, and the acceleration direction is usually the opposite direction.
(3) According to the principle of independent action of force, when Newton's second law is used to deal with the motion of an object in a plane, the force acting on the object can be decomposed orthogonally, and the component form of Newton's second law can be applied in two mutually perpendicular directions: Fx=max and Fy=may.
4. Five properties of Newton's second law:
(1) Causality: Force is the cause of acceleration.
(2) Vectorality: both force and acceleration are vectors, and the acceleration direction of an object is determined by the combined direction of external forces on the object. In the mathematical expression ∑F = ma of Newton's second law, the equal sign not only means that the values on the left and right sides are equal, but also means that the direction of acceleration of an object is the same as that of the external force.
(3) Instantaneity: When the external force acting on an object (with a certain mass) suddenly changes, the magnitude and direction of the acceleration determined by this force also suddenly changes; When the external force is zero, the acceleration is also zero, and the acceleration and the external force are in one-to-one correspondence. Newton's second law is the law of instantaneous correspondence, which shows the instantaneous effect of force.
(4) Relativity: Nature has a coordinate system. In this coordinate system, when an object is not stressed, it will maintain a uniform linear motion or a static state. This coordinate system is called inertial reference system. Both the ground and objects moving in a straight line at rest or at a constant speed relative to the ground can be regarded as inertial reference frames, and Newton's law only holds in inertial reference frames.
(5) Independence: Every force acting on an object can independently generate an acceleration, and the vector sum of the accelerations generated by each force is equal to the acceleration generated by the resultant force.
(6) Identity: A and F correspond to a certain state of the same object.
[Edit this paragraph] The scope of application of Newton's second law
(1) is only applicable to low-speed moving objects (far below the speed of light, especially in the form of F=ma).
(2) It is only applicable to macroscopic objects, and Newton's second law is not applicable to microscopic particles.
(3) The frame of reference shall be an inertial system. Not applicable to non-inertial systems.
But we can still introduce "inertial force" to make the expression of Newton's second law apply to non-inertial systems.
For example, if there is a carriage moving linearly relative to the ground with an acceleration of a, put a ball with a mass of m on the floor of the carriage, let the sum of external forces acting on the ball be f, and the acceleration of the carriage be a', and take the carriage as the reference system, obviously Newton's law of motion is not valid. namely
F=ma' does not hold.
If you use the ground as a reference system, you can get
F=ma to ground
Where a is the acceleration of the ball relative to the ground. According to the relativity of motion,
A to the ground =a+a'
Bring this formula into the above formula, there are
F=m(a+a')=ma+ma '
Then F+(-ma)=ma'
So at this point, Fo=-ma is introduced, which is called inertial force, so F+Fo=ma'
This is the expression used by Newton's second law in non-inertial system.
Therefore, when Newton's second law is applied in the non-inertial system, in addition to real and external forces, inertial force Fo=-ma must be introduced, which is opposite to the acceleration A of the non-inertial system relative to the inertial system (ground) and is equal to the mass of the studied object multiplied by A. ..