Conservation of Angular Momentum

1. The problem statement, all variables and given/known data



A merry-go-round of radius 2m has a moment of inertia 250kg*m^2, and is rotating at 10rpm on a frictionless axle. Facing the axle and initially at rest, a 25kg child hops on the edge of the merry-go-round and manages to hold on. What will be the new angular velocity of the merry-go-round after the child jumps on?



2. Relevant equations



Li (system) = Lf (system)



3. The attempt at a solution



Let g = merry-go-round and c = child.



Li = Lf, so (IW)g-initial = (IW)g+c-final.



Solving for Ic:



Ic = mr^2 = (25kg)(2m)^2 = 100kg*m^s



Solving for Ig+c:



Ig+c = Ig + Ic = 350kg*m^s



Solving for final angular velocity of system:



W(g+c)-final = (IW)g-initial / Ig+c = [(250kg*m^2)(10rpm)] / 350kg*m^s = 7.14rpm.





My question is, should I be treating the child as a point-mass, allowing me to use I = mr^2 -- or should I approximate its shape in determining I? (Treating it as a cylinder - I = .5mr^2 - I get 8.33rpm.)



Any insight into this will be much appreciated!

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Work done by a person climbing stairs

1. The problem statement, all variables and given/known data

Calculate the work done by a 52.98 kg person, who climbs a set of 0.20 m tall stairs (starting from rest) in 2.96s.

Calculate the power required to achieve this.





2. Relevant equations

w=F•d



3. The attempt at a solution

My issue with this question has been identifying the force which is acting in the situation. I know that Fg applies (mass • 9.81 m/s) and that there must be an applied force of some sort because the person is moving (working against gravity, I suppose?), but I am not sure which information I should use to calculate the "F" variable in the w=F•d equation. I think they want the power in watts (Joules per second).

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Freezing Point of Water

Why do we define the freezing point of pure water as 0°C when most pure water does not freeze at that temperature?



Instead, it can and does remain in the liquid phase down to temperatures as low as -48°C [Molinaro & Moore, 2011].



Cold-weather clouds throughout the Earth’s atmosphere consist primarily of water droplets at temperatures tens of degrees below 0°C. These droplets of liquid water are quite stable. They condense, collide, agglomerate, fragment, and vaporize—all without freezing. Most cumulonimbi (thunderheads) do not form their icy “anvil” until updraft ambient air temperatures approach -42°C.



I am well aware that the abundance of exotic (non-water) icing nuclei on the Earth’s surface brings about surface freezing in the vicinity of 0°C, but such water is hardly “pure”. Water uncontaminated by such nuclei does not freeze at 0°C.



Why then should the generally accepted scientific definition of water’s freezing point be 0°C?

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Commutation of operators

What do we mean by the two operators are commutative or non commutative? I wanted to understand the physical significance of the commutative property of the operators. We are doing the introduction to quantum mechanics and there are many things that are really confusing. Any help will be appreciated. Thanks.

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Maximum Mass You Could Boil with 1000 J of Heat (Thermodynamics)

1. The problem statement, all variables and given/known data

What is the maximum mass of ethyl alcohol you could boil with 1000J of heat, starting from 18∘C?





2. Relevant equations

Q=mcΔT



c ethyl alcohol = 2400 J/(kg*K)

T boil ethyl alcohol = 78 C = 351 K

T starting = 18 C = 291 K



3. The attempt at a solution



m=Q/(c*ΔT)



m= (2400 J)/[(2400 J/kg*K)(351 K -291 K)] = .00694 kg (or 6.94E-3 kg)



It tells me this is wrong. I am probably overlooking something quite obvious. Thanks :)

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Living in Warsaw, and proud of it :)

No, I didn't shot it. But it is not about me, it is about my city :smile:

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Quantum Entanglement on two particles

Hi.



Imagine a system of two particles, A and B, where they are entangled.

I've been studying a little bit of quantum entanglement and I understand how measurement of one property of a particle A leads us to find indirectly the value of that property to the particle B. My question is: if I act on one of the particles, let it be A, so that the particle changes in some way, will the particle B also suffer that same change? Or is quantum entanglement strictly related to measurements?



Thanks.

D.

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How are dark matter, general relativity, and standard model related?

In other words, can dark matter be reconciled with GR without drastically changing the idea that force is due to space-time curvature? and in the case of the standard model is there any thoughts of how the force of dark matter is transmitted via the exchange of a particle? It seems that this question would have to be considered in a unifying theory such as string theory, but I have never seen anybody's ideas about it.

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Angular velocity when mass is added at center of rotation

1. The problem statement, all variables and given/known data

A guy is spinning on a chair with his hands at rest on his lap. As he is spinning, a large mass drops into his hands/lap. Does the guy continue spinning at the same rate, a slower rate, or a faster rate?

This video demonstrates what happens when the guy drops mass:

http://media.pearsoncmg.com/aw/aw_0m...d/video20.html



Please do not answer the question for me, but help me understand the problem and relevant equations.





2. Relevant equations

L = Iω = m(r^2)ω -----I think this this is the equation I need....





3. The attempt at a solution

If mass is added, shouldn't ω decrease due to the conservation of angular momentum?

But I did a quick experiment with my brother and I didn't seem to slow down...

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Electric potential along the x-axis

1. The problem statement, all variables and given/known data

The electric potential along the x-axis is V=100e^(−2x/m), where x is in meters.

Find Ex at x=1.0m and Ex at x=2.1m





2. Relevant equations

V=Ed

Ex = dV/dx (?)







3. The attempt at a solution

I took the derivative of V and got (-200/m)e^(-2x/m)

I don't know what m is and I'm just not sure how I can get an integer value for Ex at x=1.0m and 2.1m

EDIT===

I assumed m=1 and got the correct answer, don't understand what m is though

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Find the maximum value?

1. The problem statement, all variables and given/known data

Given a=11+/-0.5, b=0.04562+/-0.0001, c=17200+/-100. Find the maximum value of the absolute error in a+2b-c.





2. Relevant equations

I'm absolutely stucked on this problem.





3. The attempt at a solution

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Find the orbital period

1. The problem statement, all variables and given/known data If a satellite is to orbit Earth at an altitude of 1.00x10^3 Km, what would be its orbital period? rs = 1.00x10^3 km, Mearth = 5.97x10^24 kg, Gravitational Constant = 6.67x10^-11







2. Relevant equations



T= 2∏√r^3/GM







3. The attempt at a solution rs = 0.815484549m (i converted the satellite's altitude to meters) T= 2∏√0.815484549^3/6.67x10^-11 x 5.97x10^24 = error in my calculator ):



Edit: i did not convert km into meters correctly so it would be 1 meter



2∏√1^3/6.67x10^-11 x 5.97x10^24

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Write rational function equation given graph

On The graph, the following information was given:

Point of discontinuity( -2,0) and (1,-3)

X intercept at ( 2,0)

Yintercept (0,-4)



This is what I had : (x+2)(x-2)(x-1)/ (x+2)(x-1)



But the answer is that u have to put (x+2)^2 in the numerator instead of what I had.

But I thought that the point of discontinuity was on that spot ( xintercept) and thus it would not be counted that there was an xintercept AND a point of discontinuity at that spot. Can someone explain this to me?

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Energy of a parallel plate capacitor homework

Hi all



"A parallel plate capacitor in which plates of area A are separated by a distance d, has a capacitance C = [itex]\frac{Aε_{0}ε_{r}}{d}[/itex]

It is charged to a pd V. Neglecting edge effects, derive an equation for the electric field E in the capacitor, and show that the energy stored per unit volume is w= 0.5[itex]ε_{r}ε_{0}E^{2}[/itex]"



I believe that the electric field in a capacitor to be equal to [itex]\frac{\sigma}{\epsilon_{0}}[/itex]

via Gauss Law, and using V = Ed you can then get V = [itex]\frac{\sigma d}{\epsilon_{0}}[/itex].



I have then tried to use the various equations for work done = 0.5CV^2, 0.5QV etc to no avail.



Any help much appreciated.



Thanks

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Electric field around a current carrying wire.

Does a current carrying wire create an electric field in it's vicinity?



I believe that there is no electric field created around the wire(ideal situation). That's because the current carrying wire is neutral. You can imagine electrons moving in a specific direction under the influence of the electric field(within the wire only) created by the voltage source and an equal number of +ive ions moving in the opposite direction. For a uniform wire where n(number of charge carriers per unit volume) is constant, the current carrying wire is always neutral. That's because in any volume irrespective of it's dimensions, number electrons is equal to the number of protons. They are moving in opposite directions but if you take a picture of the interior, you'll see that it holds. However, in reality, this might not hold because n might not be constant. The conductors used to make the wires are very close to the ideal state(approximate).



I also believe that we as a conductor get a shock on holding a current carrying wire not because it is charged, but due to a potential difference between the wire(high potential) and us(zero potential) which causes the electrons to move into our body and into the ground. So, there is a continuous flow of charges within our body which constitutes current.



Are there any cases wherein the current carrying wire is electrically charged?



I just want to be clear with this concept.

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A question about limit

lim_n→∞([itex]\frac{1}{n+1}[/itex]+[itex]\frac{1}{n+2}[/itex]+...+[itex]\frac{1}{4n}[/itex])

Hi, when I first looked at this limit I thought that the solution is 0, but the assistant applied Riemann Sum and she found that this limit equals to ln4. Why this limit is not 0. I'm confused. Can you help me?

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How to use QR decomposition to find eigenvalues?

1. The problem statement, all variables and given/known data

I need to understand how I would go about using QR decomposition of a matrix to find the matrix's eigenvalues. I know how to find the factorization, just stuck on how I would use that factorization to find the eigenvalues.





2. Relevant equations



A=QR where Q is an orthogonal matrix such that Qtranspose = Qinverse



3. The attempt at a solution



det(λ*I - QR) = 0? this doesn't really help.

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