Ah! How did I not see that. That makes sense.
About the potential, it makes sense to me to write it like:
U = \frac{1}{2} k(r-a)^2
so now we have
L = T-U=\frac{1}{2} m(\dot{r}^2 + r^2 \omega^2) - \frac{1}{2}k(r^2 - 2ra + a^2)
\frac{dL}{dr} = mr\omega^2 - kr + ka \frac{dL}{d\dot{r}} =...
I was referring to the actual movement of the mass when the spring extends, not the potential, but I see that this is in the xdot and ydot terms.
The potential would be 0 when r = a. So the potential you have written:
U = \frac{1}{2} k(x^2 + y^2) = \frac{1}{2} kr^2
Would not be equal...
Where in here does it take into account the kinetic energy of the spring extending or compressing? Or I think that is contained in the xdot and ydot term?
T=\frac{1}{2}m\left(\dot{x}^2+\dot{y}^2\right)
Also in the potential energy term, wouldn't a have to appear somewhere, since this is the...
The only constraint that I can think of is given in the problem, that the spring and the mass are constrained to move around the origin with angular frequency \omega.
We know that
\omega =\frac{v}{r}
So should I solve for v, which will be dependent on r, and then use that in the kinetic...
Homework Statement
A point mass m slides without friction on a horizontal table at one end of a massless spring of natural length a and spring constant k. The other end of the spring is attached to the table so that it can rotate freely without friction. The spring is driven by a motor...
Homework Statement
This is part of a lab I did, I am working on the writeup now. We placed a coil of wire inside of a Helmholtz pair, with 20V of 60Hz AC through the Helmholtz pair. The coil inside was connected to an oscilloscope and the induced voltages were recorded. I now need to...
I am a 2nd year physics undergrad and I am thinking about a switch to EE. I like the thought of grad school, maybe to be an engineer, so I want to know if my undergrad in physics is going to prepare me enough. Some of the upper year classes I will be taking are: (all 1 term classes):
E&M I...
So you're just starting out your career? Do you enjoy your job? Do you remember being in university and wondering what kind of job you will land, and how everything will work out? And if you don't mind, what is the pay like? What about for people higher up?
I just completed my first year as...
I am entering my first year of physics as an undergrad next month and I was wondering, with a BSc in physics, is it possibly to pursue EE as a graduate student, and then get employed in that field. I realize that with a physics major, I will not be very employable and will likely have to go to...
Hello all,
I recently graduated from high school, and accepted my offer to a pretty good university in the faculty of science. I am going to be majoring in physics and/or chemistry. I just want to know if it is right for me. More specifically, what do people do out there with a physics...
Wow, I didnt know U of T gives out that much money. I only applied to Western and Windsor, and Windsor gave out a lot but they are a crap school. Western only gives $2000 for having a 90% average.
The Windsor Physics degree is only a 3 year fast track or a 4 year co-op option. At Western I could double major in chemistry and physics, whereas Windsor, it would only be physics.
Why do you say that Western is not necessarily better than Windsor?
I would drive in and out of Windsor.
I would live in Rez at Western
The scholarship at windsor is
First Year: $2000
Second Year: $2000 + $2000**
Third Year: $2000 + $2000**
Fourth Year:$2000 + $2000**
The 2nd, 3rd, and 4th year are extra because I get paid to do some research...