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    Variance captured in coordinate axis.

    Hi all, Note: The text below is the motivation for my question. To jump to the question immediately, please skip to the line that says HI!!!! I have a set of data points, lets call it A, and I ran principal component analysis to get the top 3 principal components to be able to represent...
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    How to evaluate quality of correlation?

    Hi, I would like to know, how do I evaluate the quality of correlation? Specifically, I have a set of N datapoints, each represented by k features. I want to know how the k features correlate with each other, and therefore, I created a k by k correlation matrix. I am using R-value, so the...
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    Regarding Basis and Dual Basis

    Hi, I'm learning about vector spaces and I would like to ask some questions about it. Suppose I have a vector space V, and a basis for V \{v_1, ... v_n\}. Then there is a dual space V^* consisting all linear functions whose domain is V and range is ℝ. Then the space V^* has a dual basis \{x_1...
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    Information is a form of energy?

    Information is a form of energy?? Hi all, I recently read an article on economist about Maxwell's Demon. It is mentioned that someone disproved Maxwell's demon by considering the information you need to determine whether you should let the air molecule to go to the other side. This required...
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    Calculating Error

    Hi all, I am trying to use excel to do error analysis. I have a set of data points, and I have the average value and standard deviation of all the data points (which I use to plot the error bars). I want to use the excel to plot the best fit line and extreme line to get the error. However, it...
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    How does this circuit technique work?

    Hi all, Recently I came across a circuit problem: Consider a cube circuit, where there is a resistor on each of the edges (Thus there are 12 resistors in total). All resistors have resistance R. Find the effective resistance between any two adjacent points. I used the usual method of...
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    A question on Energy and System

    1. Homework Statement At t = 0, a massless bucket contains a mass M of sand. It is connected to a wall by a massless spring with constant tension T (that is, independent of length). The ground is frictionless, and the initial distance to the wall is L. At later times, let x be the distance...
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    Simple Harmonic Motion with Springs that have Mass

    Hi all, I recently learnt about simple harmonic motion. In all the questions I have done, the springs are massless. I would like to know what happens when the spring has mass. I think that if the spring has mass, then the force in the spring will also have to counteract the weight of the...
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    Trying to understand Special Relativity

    Hi, I was reading on special relativity and was trying to understand it. However, I am still not very sure about the concepts. For example, I have this problem: I have 2 spaceships, A and B, travelling towards each other. Both have rest length x and speed v, where v is near the speed of...
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    Physics Paradoxes?

    Hi, I have two questions about electromagnetism that I would like to ask. The 1st one is as follows: I have two point charged particles A and B a distance x apart. A and B exert a force on each other by Coulomb's Law, but a force is exerted on the particles to keep them apart at exactly x...
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    University Physics or Physics for Scientists and Engineers?

    Hi, I would like to ask for opinions about the above two textbooks. University Physics by Young and Freedman Physics for Scientists and Engineers by Jewett Serway I would like to ask for opinions about the above two books. I did a few problems from both books, and it seems that the problems...
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    Combinatorics Problem

    1. Homework Statement You are given n identical As and n identical Bs. You are supposed to arrange them in a circle. How many unique arrangements are there? 2. Homework Equations Use of combinatorics 3. The Attempt at a Solution At first, I tried working out the answer if I...
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    Inextensible string exerts no force?

    Hi all, I am thinking about a problem and am currently quite confused about it. Suppose I have 2 identical balls on the x-axis, tied together by a loose inextensible string. When I hit the ball on the right to the right, the string will eventually get taut and the ball on the left will get...
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    Why is acceleration constant?

    Hi, I just saw the solution to a problem I was pondering about recently and did not really understand one of the steps/assumptions they made, and therefore I hope that you guys can clarify my doubts. The question is like this, you have a block on a frictionless inclined slope of height h...
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    Minimum Velocity needed to clear a hemisphere

    1. Homework Statement There is a hemisphere of radius R metres on the ground. You are standing at the very top of the hemisphere and you kick a ball out such that it travels outwards horizontally with speed v metres per second. During the trajectory of the ball, it does not come into contact...
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    How do you see the Milky Way?

    How do you see the whole of milky way if we are in it?
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    Doubts about moment of inertia

    1. Homework Statement The polar ice caps contain about 2.3*10^19 kg of ice. This mass contributes essentially nothing to the moment of inertia of Earth because it is located at the poles, close to the axis of rotation. Because of Global warming, all the ice has melted and formed a uniform coat...
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    Mixed up with Work and Power and Force

    Hi, I have a mix-up with power and work and force too. My problems stem from this question: A plane of mass M consumes P Power in order to stay afloat. Express the power used in terms of M and other relevant constants. The more I thought about this problem, the more I got confused. It makes...
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    Math Problem

    Hi, Given that the radius of a circle is X, and the side length of a square is Y, what is the maximum number of squares you can fill inside this circle, provided that the squares do not overlap? If you know of a general formula or something, can you please tell me the proof or give me a link...
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    Mutual Inductance and Transformer Question

    Hi, I would like to ask a question about Mutual Inductance and Transformer. Suppose I have two coils N1 and N2, where N1 is the primary coil and N2 is the secondary coil that is connected in series with some resistance Rx. If I place a voltage V1 across the primary coil, the output voltage V2...
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    Electric Potential energy for geometric objects

    I recently found out how to calculate the potential energy of a charged insulated sphere of radius R and charge density rho. I would like to know how to calculate the potential energy for other geometric objects, such as a line of charges, a sheet of charges, or a pyramid of charges. I don't...
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    Simpleton's Thread with Problems

    Hi, here are a list of questions I have doubts about (I do not want to create one for every problem so as not the spam the forum) Q1. 1. Homework Statement My senior gave me this problem. Given that the Earth's radius at the equator is Re, and the radius at the poles is Rp, express the ratio...
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    Question about spherically symmetric charged objects

    Hi, I would like to ask a question about spherically symmetric charged objects. My teacher told me that you can treat spherically symmetric charged objects at point charges. However, my teacher did not prove it. I guess you have to integrate every small volume on the spherically symmetric...
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    Speed Limit to Running

    Hi all, I am doing a project on the speed limit on human sprinting. I was doing a thought experiment and then got myself confused, so I hope you guys can help me out. I assumed that there is no air resistance, and that the coefficient of friction between the ground and the foot is...
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