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Notes without questions - Department of Physics and Astronomy
Notes without questions - Department of Physics and Astronomy

PHY 231 Midterm Exam II Form 1 Name
PHY 231 Midterm Exam II Form 1 Name

Momentum
Momentum

Relevant Equations
Relevant Equations

... U1-2: Work of a non-conservative variable force ΔT = change in kinetic energy ΔVg = change in potential energy ΔVe = change in potential energy (for a spring) g = gravitational constant (9.81 meters per second squared or 32.2 feet per second squared) h = height above or below reference datum (can be ...
Problems for Mathematics of Motion: week 6
Problems for Mathematics of Motion: week 6

Rotational Motion - SFA Physics and Astronomy
Rotational Motion - SFA Physics and Astronomy

... combinations. Using Newton’s Second Law, we can write Fc = mac = mv2/r = mr2. “Centrifugal (center fleeing) force” is a fictitious force experienced by an object located in an accelerated reference frame. As viewed from the outside of the system, these “centrifugal forces” can be seen to be simple ...
Linear and angular concepts
Linear and angular concepts

Chapter_9a
Chapter_9a

... Describe the motion of the center of mass before and after the explosion. ...
Rotational Motion Practice MC Answers
Rotational Motion Practice MC Answers

Kinetics of Particles: Newton`s Second Law
Kinetics of Particles: Newton`s Second Law

... This is a diagram showing some object and the forces applied to it. It contains only forces and coordinate information, nothing else. There are only two kinds of forces to be considered in mechanics: ...
2103-617: Advanced Dynamics Handout # 2: Review of Dynamic
2103-617: Advanced Dynamics Handout # 2: Review of Dynamic

... the motion of the pendulum for any arbitrary θ (t). In addition, this system has one degree of freedom, thus only one equation of motion is needed. Specifically, the number of equations of motion used to describe the motion is equal to the number of degrees of freedom of that system. If only the sma ...
Section 1 1. What two factors (hint: they are anthropometric
Section 1 1. What two factors (hint: they are anthropometric

Homework 8    
Homework 8    

Physics 2010: Exam 3 (Final) Sample Questions - Key
Physics 2010: Exam 3 (Final) Sample Questions - Key

Impulse and Momentum
Impulse and Momentum

...  Momentum: mv, or the product of the object’s mass and the objects velocity  Impulse-momentum Theorem: FΔt= pf –pi ; The impulse on an object is equal to the object’s final momentum mines the object’s initial momentum (p= momentum) ...
Physics 161 NAME
Physics 161 NAME

The Book we used
The Book we used

... The Foucault pendulum at the Franklin Institute in Philadelphia. This type of pendulum was first used by the French physicist Jean Foucault to verify the Earth’s rotation experimentally. As the pendulum swings, the vertical plane in which it oscillates appears to rotate as the bob successively knoc ...
11-2 Vector Cross Product
11-2 Vector Cross Product

... a System of Particles; General Motion The angular momentum of a system of particles can change only if there is an external torque—torques due to internal forces cancel. ...
Conservation Of Linear Momentum
Conservation Of Linear Momentum

... The Foucault pendulum at the Franklin Institute in Philadelphia. This type of pendulum was first used by the French physicist Jean Foucault to verify the Earth’s rotation experimentally. As the pendulum swings, the vertical plane in which it oscillates appears to rotate as the bob successively knoc ...
Momentum Problems
Momentum Problems

MODULE DESCRIPTOR Code: Alt Codes: Title:
MODULE DESCRIPTOR Code: Alt Codes: Title:

... Lectures and tutorials. Tutorial sheets and other exercises will be used to provide formative assessment. Practical classes related to the reinforcement of conceptual ideas taught in this subject will be conducted and assessed in MECH102P Mechanical Engineering Practical Skills I. Assessment: Writte ...
1. A particle of mass m is projected vertically upward at z=O, with an
1. A particle of mass m is projected vertically upward at z=O, with an

MASSACHUSETTS INSTITUTE OF TECHNOLOGY
MASSACHUSETTS INSTITUTE OF TECHNOLOGY

25. Rigid Body Moving Freely
25. Rigid Body Moving Freely

Momentum
Momentum

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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.
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