Integrating to solve kinematics problem, bad or good?

[Femme_physics]

My lecturer told me that it's best not to integrate when you're a new student to kinematics because it's important to understand the principles of operation-- which is why we're not using it. On the other hand, I keep being told by this forum that calculus is the true way to fathom mechanics.

Therefor, I'm completely confuse as to how do I bridge those contradicting statements. Can anyone clear the air for me?

 

[I like Serena]

My lecturer told me that it's best not to integrate when you're a new student to kinematics because it's important to understand the principles of operation-- which is why we're not using it. On the other hand, I keep being told by this forum that calculus is the true way to fathom mechanics.

Therefor, I'm completely confuse as to how do I bridge those contradicting statements. Can anyone clear the air for me?

In the end you need to know both.

It's mostly a matter of teaching methodology.
If a teacher throws too much theory at his students too quickly, the students will become confused, and won't know what to do any more.

I think it's important that a student can find a thread in a problem and pursue that thread logically. It the student stops looking for threads, because there are simply too many, the teacher has failed.

I believe however, that if a student can and actively finds threads into problems fine, and is asking for more, there's nothing wrong with giving more!
And seeing how different methods yield the same result will enhance the understanding.

You might compare it with "voltage drops" versus "Kirchhoff's laws".
Typically you're taught "voltage drops" first to gain an intuitive understanding.
In your case you learned it the other way around.
Somehow you were stumped by the concept of voltage drops, but once you saw how Kirchhoff's laws work, I think the voltage drops fell into place!

As for kinematics. I think it's fine to learn it in the order the teacher teaches it.
But whenever you want to know more, or want to see different ways of solving them, just ask!
As long as you are the one deciding what to learn and when to learn it in a way that fits into your thinking processes, you'll find you progress optimally.

 

[Femme_physics]

If the analogy really fits "voltage drop" versus Kirchhoff's laws, then it's a must, I would say!

So, if I need to know both, and both provides me with an insight to kinematics, then I guess there's no harm in starting up with it. Although, I'll stay with the class. If, according to you, it's a "must know" in kinematics/dynamics, then I'm sure it's on the teaching plan.

Is it easier/faster to use integration to solve kinematics problems?

 

[I like Serena]

Is it easier/faster to use integration to solve kinematics problems?

For the problems you have shown so far it won't matter.
[edit] They are designed to be solved with the set of equations you have. [/edit]

What you have is a long list of different equations that you have shown in another thread.
You were kind of impressed that there were so many.

I noted at the time that they are all actually one and the same formula, just variations of it and that it was beautiful!

Once you learn more about derivation and integration in the context of kinematics, you'll see that this is the case.

Since you've shown an interest, I'll drop hints every now and then...

 

[AlephZero]

I'm not sure I agree with your teacher. If you get the mindset that mechanics is about remembering lots of formulas and choosing the right one to solve a problem, that won't get you very far.

On the other hand, it does get people started if they are weak at calculus or haven't studied it at all - i.e. "algebra based physics" rather than "calculus based physics" .

Of course there is not much point in repeatedly doing simple integrals to get results you can remember anyway (like v² = 2gh or whatever), but personally, after decades of doing dynamics "for real", I'm more confident that I can integrate things correctly than remember where every factor of 2 and 1/2 goes in a bunch of "standard" formulas.

 

[Femme_physics]

Once you learn more about derivation and integration in the context of kinematics, you'll see that this is the case.

Duly noted!

I'm not sure I agree with your teacher. If you get the mindset that mechanics is about remembering lots of formulas and choosing the right one to solve a problem, that won't get you very far.

Well, so far I've seen that there is only a velocity formula that relates acceleration and time, and a position formula that relates initial velocity, initial position, acceleration and time.

The rest of the formulas appears to be derived from these two.

On the other hand, it does get people started if they are weak at calculus or haven't studied it at all - i.e. "algebra based physics" rather than "calculus based physics" .

I believe that is the case in our class. Though we do know the basics of the integration and taking the derivative.
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But very well, I'll wait to see how things progress, thank you for your feedback. It'll be interesting for me to see how things unfold and whether I'll get back to this thread yet!

 

[NEILS BOHR]

i think you will realize it very soon that you will sometimes feel helpless without the sound knowledge of maths in physics...

 

[Studiot]

I must say I sympathise with your lecturer. There are very few parts of physics that can only be done by integration.

Most often we actually use a property of integration - that it is a summmation process.
We take a small element of something and consider some property. Then we use integration to add up all the effects of that property for every element of the something.

Surely it is more important that you understand the property than the summation process?

As an example take the usual definition/introduction to moment of inertia.

The moment of inertia about an axis is given by something like

$$I = \int\limits_0^a {2\pi \rho {r^3}} dr$$

Now isn't it more helpful to be told

Inertia is resistance to change of motion. Acceleration is a measure of change of motion.

So the effort we have to apply to change the motion along some line is the mass times the acceleration.
So mass is a measure of the inertia of a body to change of linear motion.

When we want to change the rotational motion of a body, about some axis, we have to apply a torque equal to the angular acceleration times the moment of inertia.

I think this makes the physical reality of the meaning of moment of inertia more apparent.

When you come to study impulse ( a variable force of short duration such as applied by a hammer) you will find that the impulse is defined by an integral that cannot be (directly ) evaluated.

$${\mathop{\rm Im}\nolimits} pulse = \int\limits_{{t_0}}^{{t_1}} {Fdt}$$

 

[BruceW]

Your lecturer is right, students all over the world are taught the equations of motion first, then how to get them (by using integration) later.
The reason is that new students are already very familiar with algebra, but less familiar with using integration.
Also, the integration method is the deeper physical meaning behind the equations of motion.
Generally when teaching physics, you start with the less deep stuff - just equations that predict physical phenomena. Then later you get to why the equations are true.

 

[RedX]

To be honest I probably couldn't solve some mechanics problems without integration, such as Kepler's problem. I thought that was one of the goals of mechanics, to get enough first integrals to solve the problem by quadrature.

Didn't Newton invent calculus to do mechanics?

If you're good at calculus I see no reason to not use calculus. However, a lot of physics is experimental and data collecting, and you only sample a finite number of points, so make sure you can do algebra too.