![Physics Midterm Study Guide](http://s1.studyres.com/store/data/010598627_1-ef221c60b473ec9506f3343940ae186e-300x300.png)
Part41
... Second Law for rotations: S t = Ia , let’s see if we can get a rotational energy relation. Recall that Work = F ds. If we exert a force to spin an object, the ds becomes a small arc length that is perpendicular to the radius. Recall the definition of an angle in radians: q = s/r, so that ds = r d ...
... Second Law for rotations: S t = Ia , let’s see if we can get a rotational energy relation. Recall that Work = F ds. If we exert a force to spin an object, the ds becomes a small arc length that is perpendicular to the radius. Recall the definition of an angle in radians: q = s/r, so that ds = r d ...
PHYS 221 General Physics I Course Outcome Summary Course
... Demonstrate knowledge of kinetic energy's ability to perform work. Learning Objectives a. Describe and define kinetic energy and provide application examples. b. Demonstrate the application of force to accomplish work. c. Review different types of energies. d. Identify how work is accomplished by gr ...
... Demonstrate knowledge of kinetic energy's ability to perform work. Learning Objectives a. Describe and define kinetic energy and provide application examples. b. Demonstrate the application of force to accomplish work. c. Review different types of energies. d. Identify how work is accomplished by gr ...
Rotation
... Up until now we have been looking at the kinematics and dynamics of translational motion – that is, motion without rotation. Now we will widen our view of the natural world to include objects that both rotate and translate. ...
... Up until now we have been looking at the kinematics and dynamics of translational motion – that is, motion without rotation. Now we will widen our view of the natural world to include objects that both rotate and translate. ...
here
... • Angular momentum is a measure of the spin of an object. It depends on the mass that is spinning, on the distance from the rotation axis, and on the rate of spin. • I = (mass).(radius).(spin rate) • The angular momentum in a system stays fixed, unless acted on by an outside force. • An orbiting bod ...
... • Angular momentum is a measure of the spin of an object. It depends on the mass that is spinning, on the distance from the rotation axis, and on the rate of spin. • I = (mass).(radius).(spin rate) • The angular momentum in a system stays fixed, unless acted on by an outside force. • An orbiting bod ...
Instructions Grading Scheme
... but the top of the axle will rotate along a circular path that lies in a horizontal plane. For clarity, the direction of the angular velocity vector, L, has been shown at a particular moment in time when the axle is tilted to the right by an angle [ relative to the vertical. The central axle of the ...
... but the top of the axle will rotate along a circular path that lies in a horizontal plane. For clarity, the direction of the angular velocity vector, L, has been shown at a particular moment in time when the axle is tilted to the right by an angle [ relative to the vertical. The central axle of the ...
Relativistic angular momentum
""Angular momentum tensor"" redirects to here.In physics, relativistic angular momentum refers to the mathematical formalisms and physical concepts that define angular momentum in special relativity (SR) and general relativity (GR). The relativistic quantity is subtly different from the three-dimensional quantity in classical mechanics.Angular momentum is a dynamical quantity derived from position and momentum, and is important; angular momentum is a measure of an object's ""amount of rotational motion"" and resistance to stop rotating. Also, in the same way momentum conservation corresponds to translational symmetry, angular momentum conservation corresponds to rotational symmetry – the connection between symmetries and conservation laws is made by Noether's theorem. While these concepts were originally discovered in classical mechanics – they are also true and significant in special and general relativity. In terms of abstract algebra; the invariance of angular momentum, four-momentum, and other symmetries in spacetime, are described by the Poincaré group and Lorentz group.Physical quantities which remain separate in classical physics are naturally combined in SR and GR by enforcing the postulates of relativity, an appealing characteristic. Most notably; space and time coordinates combine into the four-position, and energy and momentum combine into the four-momentum. These four-vectors depend on the frame of reference used, and change under Lorentz transformations to other inertial frames or accelerated frames.Relativistic angular momentum is less obvious. The classical definition of angular momentum is the cross product of position x with momentum p to obtain a pseudovector x×p, or alternatively as the exterior product to obtain a second order antisymmetric tensor x∧p. What does this combine with, if anything? There is another vector quantity not often discussed – it is the time-varying moment of mass (not the moment of inertia) related to the boost of the centre of mass of the system, and this combines with the classical angular momentum to form an antisymmetric tensor of second order. For rotating mass–energy distributions (such as gyroscopes, planets, stars, and black holes) instead of point-like particles, the angular momentum tensor is expressed in terms of the stress–energy tensor of the rotating object.In special relativity alone, in the rest frame of a spinning object; there is an intrinsic angular momentum analogous to the ""spin"" in quantum mechanics and relativistic quantum mechanics, although for an extended body rather than a point particle. In relativistic quantum mechanics, elementary particles have spin and this is an additional contribution to the orbital angular momentum operator, yielding the total angular momentum tensor operator. In any case, the intrinsic ""spin"" addition to the orbital angular momentum of an object can be expressed in terms of the Pauli–Lubanski pseudovector.