Chapter 4 Conservation laws for systems of particles
... The concepts of work, power and energy are among the most powerful ideas in the physical sciences. Their most important application is in the field of thermodynamics, which describes the exchange of energy between interacting systems. In addition, concepts of energy carry over to relativistic system ...
... The concepts of work, power and energy are among the most powerful ideas in the physical sciences. Their most important application is in the field of thermodynamics, which describes the exchange of energy between interacting systems. In addition, concepts of energy carry over to relativistic system ...
Angular speed - Haiku for Ignatius
... You are asked for centripetal acceleration and a comparison with g (9.8 m/s2). You are given the linear speed and radius of the motion. Use: ac = v2 ÷ r 4. Solve: ac = (10 m/s)2 ÷ (50 m) = 2 m/s2 The centripetal acceleration is about 20%, or 1/5 that of gravity. ...
... You are asked for centripetal acceleration and a comparison with g (9.8 m/s2). You are given the linear speed and radius of the motion. Use: ac = v2 ÷ r 4. Solve: ac = (10 m/s)2 ÷ (50 m) = 2 m/s2 The centripetal acceleration is about 20%, or 1/5 that of gravity. ...
Vector Algebra and Velocity
... REVIEW: Multiplication of a Vector by a Scalar The easiest type of multiplication is that of a vector by a scalar. This always produces another vector. Be careful – multiplication of a vector by a scalar is NOT the same as scalar multiplication of two vectors which is covered in Chapter 6. There are ...
... REVIEW: Multiplication of a Vector by a Scalar The easiest type of multiplication is that of a vector by a scalar. This always produces another vector. Be careful – multiplication of a vector by a scalar is NOT the same as scalar multiplication of two vectors which is covered in Chapter 6. There are ...
PPT
... Good, the moment of inertia has the smallest value for rotation about the center of mass! Any other axis will give a larger moment of inertia. When we say “moment of inertia” we’re not finished. We always have to say — or think — “moment of inertia about some particular axis of rotation”. ...
... Good, the moment of inertia has the smallest value for rotation about the center of mass! Any other axis will give a larger moment of inertia. When we say “moment of inertia” we’re not finished. We always have to say — or think — “moment of inertia about some particular axis of rotation”. ...
Solutions #9
... These forces are exerted by the rod. Since they are unequal, there would be a net horizontal force on the rod (and hence the axle) due to the masses. This horizontal force would have to be counteracted by the mounting for the rod and axle in order for the rod not to move horizontally. There is also ...
... These forces are exerted by the rod. Since they are unequal, there would be a net horizontal force on the rod (and hence the axle) due to the masses. This horizontal force would have to be counteracted by the mounting for the rod and axle in order for the rod not to move horizontally. There is also ...
Chapter 9 Clickers
... increases linearly from zero newtons to twenty-four newtons during the first two seconds. Then, the force remains constant for four seconds. During the last two seconds, the force linearly decreases to zero newtons. What is the total impulse exerted on the object? a) This cannot be determined becaus ...
... increases linearly from zero newtons to twenty-four newtons during the first two seconds. Then, the force remains constant for four seconds. During the last two seconds, the force linearly decreases to zero newtons. What is the total impulse exerted on the object? a) This cannot be determined becaus ...
1 CHAPTER 22 DIMENSIONS 22.1 Mass, Length and Time Any
... second are not so “natural” in this sense as they are “man-made”. It is true that a GeV is not particularly “natural”, but at least a system with GeV, c and ħ as fundamental quantities is certainly more “natural” than metre-kilogram-second. In any case, the dimensions of mass in this system are EV−2 ...
... second are not so “natural” in this sense as they are “man-made”. It is true that a GeV is not particularly “natural”, but at least a system with GeV, c and ħ as fundamental quantities is certainly more “natural” than metre-kilogram-second. In any case, the dimensions of mass in this system are EV−2 ...
Momentum and Its Conservation
... The first and most obvious condition is that no balls are lost and no balls are gained. Such a system, which does not gain or lose mass, is said to be a closed system. The second condition is that the forces involved are internal forces; that is, there are no forces acting on the system by objects o ...
... The first and most obvious condition is that no balls are lost and no balls are gained. Such a system, which does not gain or lose mass, is said to be a closed system. The second condition is that the forces involved are internal forces; that is, there are no forces acting on the system by objects o ...
Momentum and Its Conservation
... The first and most obvious condition is that no balls are lost and no balls are gained. Such a system, which does not gain or lose mass, is said to be a closed system. The second condition is that the forces involved are internal forces; that is, there are no forces acting on the system by objects o ...
... The first and most obvious condition is that no balls are lost and no balls are gained. Such a system, which does not gain or lose mass, is said to be a closed system. The second condition is that the forces involved are internal forces; that is, there are no forces acting on the system by objects o ...
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.