CAn any one explain to me why it is better to use angular velocitu rather than linear in circular motion???
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CAn any one explain to me why it is better to use angular velocitu rather than linear in circular motion???
Yes,
you can travel 360 degs or (2pi radians) and everybody knows although you are back in the same place you have done something.
Whereas if you are using linear and you say you have moved 25 metres where are you?
It just looks like you travelled in a straight line, are you back in the same place or not?
So it makes sense to use linear for straight lines (which is what the word linear means anyway) or angular for circular.
From mathematics point of view, since both are related to each other by the formula u=pi*D*N/60, it doesn't matter in whatever way you define.
where,
u=linear velocity, in m/s
D=diameter of wheel, in m
N=number of revolutions per minute, in rpm. (however, some speed measuring device can get you speed in rps, in such case '/60' need not be done).
Would you like to correct your formula?Quote:
Originally Posted by sramanujam
Hi, :)Quote:
Originally Posted by almirza
Angular Velocity is better than linear velocity because it help us to easy calculate the number of revolution.
Hi billco,
is there a mistake in the formula? I can't find any!
u=r*w (read omega)
but w=2*pi*N/60
Therefore, u=2*r*Pi*N/60, implies
u=[pi*Diameter*No of rev/min]/60.0 is correct. Can you please explain what's wrong in it?
It is not considered good practice to write down a formula and not explain the terms, you and I may know what the terms are/mean but the person who asked the question deserves an unambigious answer - even your latest answer does not give 'units' for 'u' and why rev/minute /60? - Revolutions per second would be more appropriate since we [generally] use the Kilogram Metre Second.Quote:
Originally Posted by sramanujam
@billco:
Thanks for pointing out your reason billco. I accept it. But when you replied "would you like to correct your formula" I thought I have done a mistake in the formula itself :!:
in circular motion the velocity, because its a vector is alwyas changing. and there is an acceleration towards the center so if you use linear velocity it would show a constant v instead of a changing one.
This is my first post. please be gentle.
Thank you
I appreciate that.
@psynapse:
Welcome to scienceforum. Your reply is interesting. Since linear displacement is defined, for circular motion, in polar coord, vectorially as x=r*cos(theta)i+r*sin(theta)j, linear velocity is obtained by differentiating linear displacement w.r.t. time.
Thus u=-r*sin(theta)*d(theta)/dt i+ r*cos(theta)*d(theta)/dt j. But d(theta)/dt=w (read omega, angular velocity).
Magnitude of u results in the equation which I've already posted.
"...if you use linear velocity it would show a constant v instead of a changing one..."
You are wrong. Vectorially u is given as a function of theta, which keeps on changing w.r.t theta, however, its magnitude remains same. Similar argument can be made if you represent in terms of angular velocity.
Keep posting :)