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notes5 Potential Energy Conservation
notes5 Potential Energy Conservation

... This indicates that the potential energy change from position 1 to position 2 (i.e., the gain) ΔU=U2-U1 is equal to negative of the work done by the gravitational force W1-2 to move the mass from position 1 to position. For the mass to gain gravitational potential energy (i.e., ΔU=U2-U1>0), gravita ...
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... always true of kinetic energy. If the kinetic energy of the bodies involved in a collision is the same before and after impact, the collision is said to be a perfectly elastic collision. If the bodies stick together after impact, the collision is said to be completely inelastic. These represent the ...
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... Newton’s three laws describe how things move and how this motion can be changed by other forces/objects Newton’s laws lead to the formulas that lets us express motion with math ...
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... divide by the denominator—the total mass will certainly be positive and will not affect the sign of the answer. So we could have done a simple mental calculation of the numerator (82  3  110  2) to figure out which football players ―wins.‖ P9.55: Most geologists believe that the dinosaurs became ...
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... P3.1d Identify the basic forces in everyday interactions. P3.2A Identify the magnitude and direction of everyday forces (e.g., wind, tension in ropes, pushes and pulls, weight). P3.2B Compare work done in different situations. P3.2C Calculate the net force acting on an object. P3.2d Calculate all th ...
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Relativistic mechanics

In physics, relativistic mechanics refers to mechanics compatible with special relativity (SR) and general relativity (GR). It provides a non-quantum mechanical description of a system of particles, or of a fluid, in cases where the velocities of moving objects are comparable to the speed of light c. As a result, classical mechanics is extended correctly to particles traveling at high velocities and energies, and provides a consistent inclusion of electromagnetism with the mechanics of particles. This was not possible in Galilean relativity, where it would be permitted for particles and light to travel at any speed, including faster than light. The foundations of relativistic mechanics are the postulates of special relativity and general relativity. The unification of SR with quantum mechanics is relativistic quantum mechanics, while attempts for that of GR is quantum gravity, an unsolved problem in physics.As with classical mechanics, the subject can be divided into ""kinematics""; the description of motion by specifying positions, velocities and accelerations, and ""dynamics""; a full description by considering energies, momenta, and angular momenta and their conservation laws, and forces acting on particles or exerted by particles. There is however a subtlety; what appears to be ""moving"" and what is ""at rest""—which is termed by ""statics"" in classical mechanics—depends on the relative motion of observers who measure in frames of reference.Although some definitions and concepts from classical mechanics do carry over to SR, such as force as the time derivative of momentum (Newton's second law), the work done by a particle as the line integral of force exerted on the particle along a path, and power as the time derivative of work done, there are a number of significant modifications to the remaining definitions and formulae. SR states that motion is relative and the laws of physics are the same for all experimenters irrespective of their inertial reference frames. In addition to modifying notions of space and time, SR forces one to reconsider the concepts of mass, momentum, and energy all of which are important constructs in Newtonian mechanics. SR shows that these concepts are all different aspects of the same physical quantity in much the same way that it shows space and time to be interrelated. Consequently, another modification is the concept of the center of mass of a system, which is straightforward to define in classical mechanics but much less obvious in relativity - see relativistic center of mass for details.The equations become more complicated in the more familiar three-dimensional vector calculus formalism, due to the nonlinearity in the Lorentz factor, which accurately accounts for relativistic velocity dependence and the speed limit of all particles and fields. However, they have a simpler and elegant form in four-dimensional spacetime, which includes flat Minkowski space (SR) and curved spacetime (GR), because three-dimensional vectors derived from space and scalars derived from time can be collected into four vectors, or four-dimensional tensors. However, the six component angular momentum tensor is sometimes called a bivector because in the 3D viewpoint it is two vectors (one of these, the conventional angular momentum, being an axial vector).
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