The second law of Newton - Zhivotov, kinetic energy and work of forces.
The second law of Newton - Zhivotov says: change of quantity of movement of a material point on a curvilinear trajectory is caused by action of driving force, which creates tangential and centripetal components of this force.
The law is expressed as follows
d (m_V)/dt = + - m_a + m __ Vw : : (1)
the mark "+" before expression ma specifies, that speed of a material point increases.
For forces of inertia the law says: change of quantity of movement of a material point creates tangential force of inertia and centrifugal force of inertia.
The law is expressed as follows
d (m_V)/dt = - + m_a - m __ Vw : :.. (2)
the mark "-" before expression ma specifies, that speed of a material point increases.
Kinetic energy of a material point and work of forces.
We admit, that the material point under action of forces goes on a curvilinear trajectory and for some time dt passes distance dS.
The right and left part of expression (1) on dS. We have
d (m_V) dS/dt = + - m_a dS + m __ Vw dS : :.. (3)
or in a vector kind
m_V dV = + - m_a dS + m __ V2 db : : : (4)
b - a corner between instant radiuses of curvature of a trajectory at moving a material point from one point of a trajectory in other point in time dt.
If the material point in time t* - to has passed a way equal S, that, беря the certain integral, we have
mV * ^ 2/2 - mVo2/2 = + - ma S + Ф (from 0 up to b) mV2 db : : (5)
or
mV * ^ 2/2 - mVo2/2 = + - Aл + An : :. (6)
where
It is scarlet - work of tangential forces.
An - work of centripetal forces.
In expression (5) change of kinetic energy of a material point and work of forces are scalar sizes.
Absence of driving centripetal forces is replaced with forces of reaction and demands the appendix of additional tangential force. Therefore work of centripetal forces in practice is compensated by work of additional tangential force.
Consequences of specification of the second law of Newton, concept of kinetic energy and work of force concern mechanics, hydrodynamics, theories of fluctuations and rotations of ph.
Earlier I tried to state proofs of the second law of Newton - Zhivotov.
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