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Old Sep 20th 2011, 02:33 PM   #1
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Is kinematics a special case of f=mA?

Hi, Physics presents kinematics as derivative relations of position, velocity, acceleration (subject to initial conditions) of some hypothetically physical (real) object through real space. Kinematics is about unmotivated movement. Forces are not mentioned in the "real" HS kinematics problems of children skating, cars on roads... et al, whatsoever.

Does kinematics have a physical principal (relating it to reality?). Is anything is conserved, kinematically? What is the origin of this big section of HS physics? Was there kinematics before f=mA? Is kinematics calculus, not physics?

I searched, read books... I think kinematics is about (...model of reality) a BODY, with the condition that acceleration of that body is constant. The idea, from Newton as: A = f/m with the force being constant in mag and direction and mass being constant as a scalar. Hmm, methinks there are no "kinematics on a circle" HS problems, if so, please tell me where?

Thanks, GymBeaux
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Old Sep 21st 2011, 02:22 PM   #2
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Kinematics is about partcle motion, and not about forces that cause the particle to move. It's not a "special case" for F=ma, as it doesn't involve forces at all. The fundamental mathematics behind it is 3-dimensional calculus relating the coordinates of a particle's position and the rate of change of those coordiantes versus time. I would agree that it is more mathematics than physics, and there are all sorts of kinematics taught in college and graduate school level math courses.

You ask does it relate to reality - not sure what you mean, but presumably you can use the equations to determine a particle's motion, so as long as the conditions are properly defined then yes, it's real.

Kinematics does not require that acceleration is held constant. Consider for example the motion of a mass on a spring - we typically describe its motion as suinusoidal, and hence the velocity and acceleration are phase-shifted sinusoidal functions as well. And as for kinematics on a circle - consider equations of circular motion typuically taught in advanced high school physics such as v = wr, where "w" is the rotational velocy (typically written as omega), or a = w^2r. These are kinematic equations involving circular motion.

One final clarification: the fundamental equation made famous by Newton was not F=ma where m is constant, but rather the more general form F=d(mv)/dt. Hence Force = rate of change of momentum, where both mass and velocity are functions of time. Expanded you get F(t) = m(t) dv/dt + v(t) dm/dt. With this form you can delve into how acceleration changes as mass changes. Classic example - consider a rocket with a fixed amount of thrust (F constant) that loses mass as it burns its fuel. But the math can get messy and complicated, so for simplicity in most highschool level homework problems you assume mass is constant, so that dm/dt is zero and you can work with the simpler equation F = ma.

Last edited by ChipB; Sep 26th 2011 at 01:40 PM.
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Old Sep 21st 2011, 04:02 PM   #3
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Thanks, ChipB

Thanks, I'll think it over. GymBeaux.
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