 #1
LCSphysicist
 634
 153
 Homework Statement:

Smooth rod OA of length l rotates around a point O in a horizontal plane with a
constant angular velocity $\delta$. The bead is fixed on the rod at a distance a from
the point O. The bead is released, and after a while, it is slipping off the rod. Find its
velocity at the moment when the bead is slipping?
 Relevant Equations:
 .
I have tried to solve this problem using the lagrangean approach: $$L = T  V = m((\dot r)^2 + (r \dot \theta)^2)/2  0 = m((\dot r)^2 + (r \delta)^2)/2  0 $$
The problem is that the answer i got is the right answer at the smooth rod referencial, that is, at the non inertial frame.
Now we can easily translate my answer of v to the inertial frame, but that is not the point of my question. The point is, when did i have assumed i was at the rod frame? That is, i have just written the kinect energy in polar coordinates, so instead of $$\sum m x_i x^{i} / 2$$ i have written it in polar language. All of sudden, am i now in a non inertial frame?
Do polar coordinates are by definition non inertial?
Should have a potential here? I can't see where does it come from. In fact, another point i can't understand is, in a inertial frame there is not a potential energy, and in fact i have used (V=0). But yet, my answer is given in a non inertial frame...
The problem is that the answer i got is the right answer at the smooth rod referencial, that is, at the non inertial frame.
Now we can easily translate my answer of v to the inertial frame, but that is not the point of my question. The point is, when did i have assumed i was at the rod frame? That is, i have just written the kinect energy in polar coordinates, so instead of $$\sum m x_i x^{i} / 2$$ i have written it in polar language. All of sudden, am i now in a non inertial frame?
Do polar coordinates are by definition non inertial?
Should have a potential here? I can't see where does it come from. In fact, another point i can't understand is, in a inertial frame there is not a potential energy, and in fact i have used (V=0). But yet, my answer is given in a non inertial frame...