# 1st year question

#### disease

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Dynamics is more general than kinematics.

Why is this true?

Because kinematics only explains how things move, and not why.

Hmm. Kinematics explains energy in terms of displacement(s), dynamics in terms of (something else).

Both are explanatory, the 'why' of energy doesn't really enter into it - both are a kind of mechanical or mathematical explanation for potentials and 'how' they move. Both are about conservation of something, but a different something.

disease:

Perhaps you ought to say what you understand the terms "kinematics" and "dynamics" to mean.

I understand kinematics to be about conserved forces, or that displacements and positions in kinematics are conserved as forces. This includes the idea of equal forces and stasis or equilibrium.
Dynamics is about conserved momentum, or that mass and energy are conserved, this doesn't need 'forces' and also implies that mass and energy (being invariant in any momentum exchange) are equivalent.

I understand kinematics to be about conserved forces, or that displacements and positions in kinematics are conserved as forces.

"Kinematics" in physics refers to the description of motion without reference to forces or masses.

"Dynamics" is the study of what makes things move, or the causes of motion - i.e. forces.

Kinematics doesn't make any reference to forces? Or to masses?

Can you show me an example or two of kinematic formulas for some systems, that avoid forces, at least? Is kinematics tied to laws of motion, and is motion because of forces and displacements? Or is it because of momentum?

Dynamics is derived from kinematics, and from electromagnetics, and a few others.
This is why it's more general.
Dynamics, as the conservation of momentum, does not require any 'forces', but does explain them. Or it can be generalised to be force-free.

Kinematics doesn't make any reference to forces? Or to masses?

That's right.

Can you show me an example or two of kinematic formulas for some systems, that avoid forces, at least?

The constant-acceleration formulae are an example:

$$s = s_0 + ut + (1/2)at^2$$
$$v = u + at$$
$$2as = v^2 - u^2$$
$$s = (1/2)(u+v)t$$

Is kinematics tied to laws of motion, and is motion because of forces and displacements? Or is it because of momentum?

All kinematics does is to describe motion quantitatively, without reference to forces or conservation laws.

Galileo started the ball rolling (literally) with his analysis of motion under gravity and in free fall.

Dynamics is derived from kinematics, and from electromagnetics, and a few others.

No. Dynamics requires a separate set of postulates, such as Newton's laws of motion, which in effect define things like forces.

Dynamics, as the conservation of momentum, does not require any 'forces', but does explain them. Or it can be generalised to be force-free.

I'm not sure exactly what you mean by this.

OK, here's how it goes according to my paradigm, which appears to be inconsistent with James R's.

Kinematics describes motion, in terms of displacements. These displacements are the result of forces. Kinematics describes the conservation of forces.

Dynamics (which is more general) describes momentum. It's a description of conservation in terms of mass and 'energy'.
"Kinematics" in physics refers to the description of motion without reference to forces or masses.
Sorry, kinematics describes motion (of masses) in terms of displacements and forces.
"Dynamics" is the study of what makes things move, or the causes of motion - i.e. forces.
Nope, dynamics is the explanation of momentum in terms of mass or other potentials that 'have' energy, forces are not a part of momentum exchanges.

Kinematics is the study of motion, dynamics is the study of momentum, so is more general.

What would you say are the kinematics of SHM, and the dynamics? How equivalent or not, are the definitions of either, or where do they 'join up'?
(This was the original question I saw somewhere - give a definition for both, and describe how equivalent they are)

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disease:

This seems a silly argument. Just grab the nearest dictionary, look up the word "kinematics" and tell me what it says.

I've got an undergrad Physics book, will that do? Would what it says be possibly a 'silly argument'?

Your contention that kinematics is independent of forces, which are a part of dynamics, is exactly backwards I think. You posted equations that show kinematics is a description of displacements, as I noted, and accelerations, which are forces divided by masses, that accelerate (under the forces).

"The study of motion is called kinematics, a word derived from the Greek kinema, meaning motion"
-- Alonso & Finn, Physics 1975 ed.
" ...a branch of dynamics that deals with aspects of motion apart from considerations of mass and force"
--Webster's online

That last is really only true in the sense displacements replace forces and accelerations replace mass, "apart from" does not mean "independent of" in this definition.

and:
Dynamics:

"1 : a branch of mechanics that deals with forces and their relation primarily to the motion but sometimes also to the equilibrium of bodies 2 : a pattern or process of change, growth, or activity <population dynamics> 3 : variation and contrast in force or intensity (as in music) "
--Webster's online
This is correct in that motion is tied to mechanics, but I don't agree completely with 'forces and their relation", because dynamics is about "momentums and their relation"

But this is getting silly, why not try to answer the question: "Describe SHM in kinematic and dynamic terms. How equivalent are the descriptions?"
And the question left dangling, which might not be a question: "Why is dynamics more general than kinematics"?

Kinematics is a way you derive equations of motion only relying on geometrical considerations and sometimes on very simple dynamics (like a freely falling body near the surface of the Earth where the surface of the Earth is considered flat). Dynamics arises when you call for something extra (like force, energy etc) in order to derive equations of motion. There is no absolute boundary between the two, and in fact there is a belief that at fundamental level everything is kinematic, which seems true for Yang-Mills and gravitational fields separately at least.

James is absolutely correct. Kinematics is simply a mathematical description of motion in terms of velocity and acceleration. What causes the acceleration is not a concern in kinematics. Dynamics studies what causes those accelerations to happen -- i.e., forces.

Don't believe me? Use google to find the answer. Here, for example: http://id.mind.net/~zona/mstm/physics/mechanics/mechanics.html.

I'll describe the difference in terms of uniform circular motion. Kinematically, circular motion (about the origin for simplicity) results when an object undergoes a constant radial acceleration of the form

$${\mathbf a} = - {\mathbf r} \omega^2$$

and the object has a velocity normal to the radial vector and equal in magnitude to

$$v = r\omega$$

Dynamically, circular motion (about the origin for simplicity) results when an object undergoes a constant radial force of the form

$${\mathbf F} = - F \hat{\mathbf r}$$

and the object has a velocity normal to the radial vector and equal in magnitude to

$$v = \sqrt{\frac{Fr}{m}}$$

Superficially, there's not much difference. However, the kinematic description doesn't care what causes the acceleration to occur. A ball tied to a string, a car driving around a circular track, or a planet in a circular orbit all obey the same kinematic relationship. The dynamic description does care.

You all seem to be missing the point.

Why is a dynamic description more general, and why would a question be asked about how equivalent kinematic and dynamic models are?

Forces are what connects the two, Newton's laws of motion go from velocity and acceleration to momentum, although you can start at the other end because of a certain symmetry, right? If you start with the general conservation of energy as momentum, you can derive kinematics. Dynamics derive forces according to causal Newtonian mechanics, and kinematics 'uses' forces as accelerations, which are changes in velocity. Changes are displacements, and you can represent positional displacements the same way.

Is Fourier harmonic representation dynamic or kinematic?

Because dynamics is more flexible. For example, imagine you want to describe the motion of a small mass connected to a fixed centre by a hard but light metal rod. One way to use kinematics would be to simply add a constraint that the distance from the mass to the centre is equal to a given fixed value (the length of the rod). But if you have to take into account the elasticity of the rod, you would use dynamics. The above kinematic description will be recovered if you take a limit that the stiffness of the rod tends to infinity.

Hah.
Dynamics describes changes in energy as momentum. Kinematics describes changes in position, velocity, and acceleration.

We are simply talking past each other, aren't we?

No. Your comment about elasticity in fact describes a dynamic 'property' of something.
Kinematics as you also say, requires a position or a length.

Kinematics is a description of changes, but derives them from static variables (position, velocity, acceleration).
Dynamically, an elastic rod will have a static elastic constant, which determines how much its energy can change.

I think it is enough if you understand these concepts on intuitive level even if you don't have a precise definition.

Maybe that's why it's a question for 1st years.