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- https://phys.libretexts.org/Bookshelves/Relativity/General_Relativity_(Crowell)/06%3A_Vacuum_Solutions/6.E%3A_Vacuum_Solutions_(Exercises)Show that in some other frame such as the rest frame of the sun, in which the planet has speed u toward the incoming probe, the maneuver adds 2u to the speed of the probe. (b) Suppose that we replace ...Show that in some other frame such as the rest frame of the sun, in which the planet has speed u toward the incoming probe, the maneuver adds 2u to the speed of the probe. (b) Suppose that we replace the planet with a black hole, and the space probe with a light ray.
- https://phys.libretexts.org/Bookshelves/Relativity/General_Relativity_(Crowell)/05%3A_CurvatureGeneral relativity describes gravitation as a curvature of spacetime, with matter acting as the source of the curvature in the same way that electric charge acts as the source of electric fields. Our ...General relativity describes gravitation as a curvature of spacetime, with matter acting as the source of the curvature in the same way that electric charge acts as the source of electric fields. Our goal is to arrive at Einstein’s field equations, which relate the local intrinsic curvature to the locally ambient matter in the same way that Gauss’s law relates the local divergence of the electric field to the charge density.
- https://phys.libretexts.org/Courses/Joliet_Junior_College/JJC_-_PHYS_110/02%3A_Book-_Conceptual_Physics_(Crowell)/2.12%3A_Electromagnetism/2.12.03%3A_Magnetic_Fields_by_Ampere's_LawContributors and Attributions Benjamin Crowell (Fullerton College). Conceptual Physics is copyrighted with a CC-BY-SA license.
- https://phys.libretexts.org/Courses/Joliet_Junior_College/JJC_-_PHYS_110/02%3A_Book-_Conceptual_Physics_(Crowell)/2.12%3A_Electromagnetism/2.12.01%3A_More_About_the_Magnetic_FieldThe electron is a single particle, not a steady current, but again we throw caution to the winds, and estimate the current it creates as \(e/\Delta t\), where \(\Delta t\), the time for one orbit, can...The electron is a single particle, not a steady current, but again we throw caution to the winds, and estimate the current it creates as \(e/\Delta t\), where \(\Delta t\), the time for one orbit, can be estimated by dividing the size of the atom by the electron's velocity. (This is only a rough estimate, and we don't know the shape of the orbit, so it would be silly, for instance, to bother with multiplying the diameter by \(\pi\) based on our intuitive visualization of the electron as moving …
- https://phys.libretexts.org/Courses/Joliet_Junior_College/JJC_-_PHYS_110/02%3A_Book-_Conceptual_Physics_(Crowell)/2.12%3A_Electromagnetism/2.12.04%3A_Ampere's_Law_In_Differential_Form_(Optional)The differential form of Gauss' law is more physically satisfying than the integral form, because it relates the charges that are present at some point to the properties of the electric field at the s...The differential form of Gauss' law is more physically satisfying than the integral form, because it relates the charges that are present at some point to the properties of the electric field at the same point. First we find the orientation of the curl-meter that gives the strongest torque, and then we define the direction of the curl vector using the right-hand rule shown in figure a/3.
- https://phys.libretexts.org/Courses/Joliet_Junior_College/JJC_-_PHYS_110/02%3A_Book-_Conceptual_Physics_(Crowell)/2.11%3A_Fields/2.11.01%3A_Fields_of_ForceImagine, for the sake of argument, that they can do this so quickly that each magnet is reversed while the force signal from the other is still in transit. (For a more realistic example, we'd have to ...Imagine, for the sake of argument, that they can do this so quickly that each magnet is reversed while the force signal from the other is still in transit. (For a more realistic example, we'd have to have two radio antennas, not two magnets, but the magnets are easier to visualize.) During the flipping, each magnet is still feeling the forces arising from the way the other magnet used to be oriented.
- https://phys.libretexts.org/Courses/Joliet_Junior_College/JJC_-_PHYS_110/02%3A_Book-_Conceptual_Physics_(Crowell)/2.14%3A_Quantum_Physics/2.14.03%3A_Matter_As_a_WaveRoughly speaking, we'd expect a neighboring pair of hydrogen atoms, A and B, to exert no force on each other at all, attractive or repulsive: there are two repulsive interactions (proton A with proton...Roughly speaking, we'd expect a neighboring pair of hydrogen atoms, A and B, to exert no force on each other at all, attractive or repulsive: there are two repulsive interactions (proton A with proton B and electron A with electron B) and two attractive interactions (proton A with electron B and electron A with proton B). The repulsion between the electrons would not be as strong, because each electron ranges over a large area, and is not likely to be found right on top of the other electron.
- https://phys.libretexts.org/Courses/Joliet_Junior_College/JJC_-_PHYS_110/02%3A_Book-_Conceptual_Physics_(Crowell)/2.04%3A_Conservation_of_Momentum/2.4.E%3A_ProblemsLet \(x\) be the length of the rope that is hanging over the edge at a given moment in time. (a) Show that \(x\) satisfies the equation of motion \(d^2x/dt^2=gx/L\). [Hint: Use \(F=dp/dt\), which allo...Let \(x\) be the length of the rope that is hanging over the edge at a given moment in time. (a) Show that \(x\) satisfies the equation of motion \(d^2x/dt^2=gx/L\). [Hint: Use \(F=dp/dt\), which allows you to handle the two parts of the rope separately even though mass is moving out of one part and into the other.] (b) Give a physical explanation for the fact that a larger value of \(x\) on the right-hand side of the equation leads to a greater value of the acceleration on the left side. (c) W…
- https://phys.libretexts.org/Courses/Joliet_Junior_College/JJC_-_PHYS_110/02%3A_Book-_Conceptual_Physics_(Crowell)/2.08%3A_Relativity/2.8.04%3A_General_Relativity_(optional)What you've learned so far about relativity is known as the special theory of relativity, which is compatible with three of the four known forces of nature: electromagnetism, the strong nuclear force,...What you've learned so far about relativity is known as the special theory of relativity, which is compatible with three of the four known forces of nature: electromagnetism, the strong nuclear force, and the weak nuclear force. Gravity, however, can't be shoehorned into the special theory. In order to make gravity work, Einstein had to generalize relativity. The resulting theory is known as the general theory of relativity. Conceptual Physics is copyrighted with a CC-BY-SA license.
- https://phys.libretexts.org/Courses/Skyline/Survey_of_Physics/01%3A_Mass_and_Inertia/1.05%3A_FootnotesYou might think intuitively that the recoil velocity should be exactly one fourth of a meter per second, and you'd be right except that the wagon has some mass as well. The argument only fails for obj...You might think intuitively that the recoil velocity should be exactly one fourth of a meter per second, and you'd be right except that the wagon has some mass as well. The argument only fails for objects light enough to be affected appreciably by air friction: a bunch of feathers falls differently if you wad them up because the pattern of air flow is altered by putting them together.
- https://phys.libretexts.org/Courses/Joliet_Junior_College/JJC_-_PHYS_110/02%3A_Book-_Conceptual_Physics_(Crowell)/2.12%3A_Electromagnetism/2.12.02%3A_Magnetic_Fields_by_SuperpositionContributors and Attributions Benjamin Crowell (Fullerton College). Conceptual Physics is copyrighted with a CC-BY-SA license.
