Circular Motion

[man0005]

Hey guys,

Just a quick question regarding circular motion. SHould I bother to attempt to understand the theory behind it or is it enough in SACS/exams to just know how to use the formulae?

[pi]

Always learn the theory, because the exam is not just crunching numbers

[man0005]

ah :/
can you help me then? :S
what does it mean when it says
The instantaneous velocity can be found by making the time intervals get smaller and smaller until you reach the limit?

[kamil9876]

You should probably include the context (or provide the whole page etc) so that people know what you are talking about. But since I am such a brilliant mind reader it is probably referring to how you can measure the instantaenous velocity as by making very small. Of course this just gives an average velocity over this tiny interval but it is a very close approximation of the actual velocity at that instant. (if you know what differentiation is this is pretty much it). Indeed this isn't just circular motion but a fact about velocity in general that you should know.

[man0005]

oh its basically just finding the instaneous gradient with the tangent line?

[schnappy]

If you had a v-t graph yes. But I don't think this sort of thing is relevant to Unit 3 physics...(I don't really see the application in this context?) but given a diagram you should be able to draw arrows for the net force, acceleration, velocity.

[pHysiX]

from my understanding of circular motion:

when we are travelling in a circular path, we are accelerating. Accelerating in the sense that our direction is constantly changing. I do not have a reference on hand, but it should be on wikipedia: by adding up the vectors acting on a particle in circular motion, we see that the resultant vector is the tangent to the circular path at one point. Point: Our direction of motion/velocity is constantly changing as it is tangential to our circular path.

Because our resulting vector (velocity vector) is a tangent to the circular path, it is in essence an instantaneous velocity; the velocity at one point, because keep in mind that the next instant, our tangent changes, thus our change in velocity and acceleration.

An instantaneous velocity is easily understood if you do calculus. The instantaneous is basically the gradient of a displacement vs time graph at one specific point. Now, to find a gradient, we would use rise over run of two points, but that would result in an average speed of two points. However, as we use two points that are closer and closer together, it will eventually bring us to a gradient of a single point, i.e. the instantaneous velocity of the point of interest. In reality, we use a limit. We use a limit to analyse the behaviour of our gradient as we get closer and closer to finding the gradient of that one point.

(Use the Essentials methods book to understand this, it has a diagram of why a derivative is ; ignore the vinculum on the lim thingo. I can't format it well )

my explanation there is pretty confusing i must admit, but i hope it helps

[man0005]

thanks for that guys! really helped me

[moekamo]

ignore the vinculum on the lim thingo. I can't format it well )

this is the code for future reference:

Code: [Select]

[tex]\lim_{h \to 0}[/tex]

[pHysiX]

ignore the vinculum on the lim thingo. I can't format it well )

this is the code for future reference:

Code: [Select]

[tex]\lim_{h \to 0}[/tex]

fkn love ya mate