Physics 505 Fall 2007 Homework Assignment #4 — Solutions

... Finally, we consider the case α → π, when the spherical cap becomes very large. In this case, let α = π − β where β is the angle of the south polar cap. The Legendre polynomial expansion is now Pl (cos α) = Pl (cos(π − β)) = Pl (− cos β) ≈ Pl (−1 + 21 β 2 ) ≈ (−1)l + 12 β 2 Pl0 (−1) Note that the l ...

... Finally, we consider the case α → π, when the spherical cap becomes very large. In this case, let α = π − β where β is the angle of the south polar cap. The Legendre polynomial expansion is now Pl (cos α) = Pl (cos(π − β)) = Pl (− cos β) ≈ Pl (−1 + 21 β 2 ) ≈ (−1)l + 12 β 2 Pl0 (−1) Note that the l ...

pdf - arXiv

... Lifshitz proposed that this effect comes from fluctuating sources of the electromagnetic field inside the interacting objects. There were another important contributions in the field, the result of Boyer [16] of the Casimir energy of an spherical shell has also an historical importance, as the deriv ...

... Lifshitz proposed that this effect comes from fluctuating sources of the electromagnetic field inside the interacting objects. There were another important contributions in the field, the result of Boyer [16] of the Casimir energy of an spherical shell has also an historical importance, as the deriv ...

ABSTRACT PHENOMENOLOGICAL ASPECTS OF HEAVY QUARK SYSTEMS

... well-defined expansion. However, the perturbative expansion produced by effective theories is still susceptible to the standard problems of expansions. The expansion, and thereby the effective theory, will break down when either the expansion parameter can no longer be treated as small or the coeffi ...

... well-defined expansion. However, the perturbative expansion produced by effective theories is still susceptible to the standard problems of expansions. The expansion, and thereby the effective theory, will break down when either the expansion parameter can no longer be treated as small or the coeffi ...

Engineering Design B Sample Title [ftp_tt]

... be treated as a single particle. Such a view, however, is not always possible, and a body, in general, should be treated as a combination of a large number of particles. The size of the body will have to be taken into consideration, as well as the fact that forces will act on different particles and ...

... be treated as a single particle. Such a view, however, is not always possible, and a body, in general, should be treated as a combination of a large number of particles. The size of the body will have to be taken into consideration, as well as the fact that forces will act on different particles and ...

Electrodynamic tether microsats at the giant planets

... . The maximum is always unstable, any kinetic mechanism for dissipation driving the satellite away from rigid-body motion at a(max), on either side of it. (Dissipation is due to tidal forces in case of natural moons; Pluto’s Charon, has reached the stable mech-minimum ...

... . The maximum is always unstable, any kinetic mechanism for dissipation driving the satellite away from rigid-body motion at a(max), on either side of it. (Dissipation is due to tidal forces in case of natural moons; Pluto’s Charon, has reached the stable mech-minimum ...

Electrostatic forces for satellite swarm navigation and

... In this work the concept of Satellitron Satellites, i.e. a swarm of satellites controlled by a hybrid thrusting electrostatic actuation system is assessed. The work described in this document is twofold. On one side the propulsion system is investigated. To this end first a model of the interaction ...

... In this work the concept of Satellitron Satellites, i.e. a swarm of satellites controlled by a hybrid thrusting electrostatic actuation system is assessed. The work described in this document is twofold. On one side the propulsion system is investigated. To this end first a model of the interaction ...

Geophysics :: 1. Gravity methods

... 2. INTRODUCTION TO THE MATHEMATICAL AND pHYSICAL BASIS OF gRAvITY If the Earth were a perfect sphere without rotation and if it were completely homogeneous in composition, the gravity field at the surface would be the same everywhere. This attraction force can be calculated on the basis of Newton’s ...

... 2. INTRODUCTION TO THE MATHEMATICAL AND pHYSICAL BASIS OF gRAvITY If the Earth were a perfect sphere without rotation and if it were completely homogeneous in composition, the gravity field at the surface would be the same everywhere. This attraction force can be calculated on the basis of Newton’s ...

AP Physics C – Practice Workbook – Book 1

... they appear. Within each section, the symbols used for the variables in that section are defined. However, in some cases the same symbol is used to represent different quantities in different tables. It should be noted that there is no uniform convention among textbooks for the symbols used in writi ...

... they appear. Within each section, the symbols used for the variables in that section are defined. However, in some cases the same symbol is used to represent different quantities in different tables. It should be noted that there is no uniform convention among textbooks for the symbols used in writi ...

General Physics I - Dr. David G. Simpson

... 16.1 Mass Suspended by Two Ropes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.2 The Pulley . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.3 The Elevator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

... 16.1 Mass Suspended by Two Ropes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.2 The Pulley . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.3 The Elevator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Rigid Body Motion - BlackHC's Adventures in the Dev World

... they are all linked together by their constant distance to each other. We will use this to deduce many important properties of rigid bodies. We will see later that many properties of the whole rigid body are made up of the sum of its particles. The mass of the rigid body for example is: ...

... they are all linked together by their constant distance to each other. We will use this to deduce many important properties of rigid bodies. We will see later that many properties of the whole rigid body are made up of the sum of its particles. The mass of the rigid body for example is: ...

Rigid Body Motion Full Version as PDF

... they are all linked together by their constant distance to each other. We will use this to deduce many important properties of rigid bodies. We will see later that many properties of the whole rigid body are made up of the sum of its particles. The mass of the rigid body for example is: ...

... they are all linked together by their constant distance to each other. We will use this to deduce many important properties of rigid bodies. We will see later that many properties of the whole rigid body are made up of the sum of its particles. The mass of the rigid body for example is: ...

Rigid Body Motion Presentation as PPTX

... body->linearMomentum.integrate(timeStep, totalForce); body->angularMomentum.integrate(timeStep, totalMoment); body->velocity = body->linearMomentum / body->mass; body->angularVelocity = body->invInertiaTensor * body->angularMomentum; body->position.integrate(timeStep, body->velocity); body->rotation ...

... body->linearMomentum.integrate(timeStep, totalForce); body->angularMomentum.integrate(timeStep, totalMoment); body->velocity = body->linearMomentum / body->mass; body->angularVelocity = body->invInertiaTensor * body->angularMomentum; body->position.integrate(timeStep, body->velocity); body->rotation ...

Document

... Members of the SCHOLAR Forum may reproduce this publication in whole or in part for educational purposes within their establishment providing that no profit accrues at any stage, Any other use of the materials is governed by the general copyright statement that follows. All rights reserved. No part ...

... Members of the SCHOLAR Forum may reproduce this publication in whole or in part for educational purposes within their establishment providing that no profit accrues at any stage, Any other use of the materials is governed by the general copyright statement that follows. All rights reserved. No part ...

3 EQUILIBRIUM - Chulalongkorn University: Faculties and

... • Show all the forces and couple moments acting on the body. • Label all the loadings and specify their directions relative to the x, y axes. The sense of a force or couple moment having an unknown magnitude but known line of action can be assumed. • Indicate the dimensions of the body necessary for ...

... • Show all the forces and couple moments acting on the body. • Label all the loadings and specify their directions relative to the x, y axes. The sense of a force or couple moment having an unknown magnitude but known line of action can be assumed. • Indicate the dimensions of the body necessary for ...

CHAPTER 1 Introduction /Basic concept

... A particle may be defined as a body (object) has mass but no size (neglected), such body cannot exists theoretically, but when dealing with problems involving distance considerably larger when compared to the size of the body. For example a bomber aeroplane is a particle for a gunner operating from ...

... A particle may be defined as a body (object) has mass but no size (neglected), such body cannot exists theoretically, but when dealing with problems involving distance considerably larger when compared to the size of the body. For example a bomber aeroplane is a particle for a gunner operating from ...

Rotating White Dwarfs and Neutron Stars in - Padis

... for their mass. In a wider sense, the class of compact objects is often defined to contain collectively planet-like objects, white dwarfs, neutron stars, other exotic dense stars, and black holes. It is well known that Newtonian theory of gravitation provides an adequate description of the gravitati ...

... for their mass. In a wider sense, the class of compact objects is often defined to contain collectively planet-like objects, white dwarfs, neutron stars, other exotic dense stars, and black holes. It is well known that Newtonian theory of gravitation provides an adequate description of the gravitati ...

R - IBPhysics2016

... potential gradient is zero somewhere in between the two masses. SOLUTION: Remember that the gravitational potential gradient g = –∆Vg / ∆r is just the slope of the surface. The saddle point’s slope is zero. Thus g = 0 there. ...

... potential gradient is zero somewhere in between the two masses. SOLUTION: Remember that the gravitational potential gradient g = –∆Vg / ∆r is just the slope of the surface. The saddle point’s slope is zero. Thus g = 0 there. ...

Two-point microrheology and the electrostatic analogy

... and its surrounding pocket, the electric field due to this charge distribution is simply that of a unit charge at the center of the sphere one. We now consider the potential of sphere two in this electric field. Because the spheres are conductors, the potential of sphere two is the same as the poten ...

... and its surrounding pocket, the electric field due to this charge distribution is simply that of a unit charge at the center of the sphere one. We now consider the potential of sphere two in this electric field. Because the spheres are conductors, the potential of sphere two is the same as the poten ...

Separation of Variables and a Spherical Shell with Surface Charge

... where there is no charge (like r < R and r > R), and then “patch them together” where those regions overlap (r = R in this case, where the charge is located). We’re motivated to approach the problem this way because Laplace’s equation for azimuthally symmetric problems can be solved quite generally ...

... where there is no charge (like r < R and r > R), and then “patch them together” where those regions overlap (r = R in this case, where the charge is located). We’re motivated to approach the problem this way because Laplace’s equation for azimuthally symmetric problems can be solved quite generally ...

details - Aksheyaa College of Engineering

... How will you find moment of a force about a given axis in three dimensions?. A semi circular lamina having a radius 100 mm is located in the xy plane such that its diametric edge coincides with y-axis. Determine the x coordinates of its centroid. UNIT-IV (DYNAMICS OF PARATICLES) A particle is projec ...

... How will you find moment of a force about a given axis in three dimensions?. A semi circular lamina having a radius 100 mm is located in the xy plane such that its diametric edge coincides with y-axis. Determine the x coordinates of its centroid. UNIT-IV (DYNAMICS OF PARATICLES) A particle is projec ...

B - fmcet

... 55. A force (10i + 20j – 5k) N applied at A (3,0,2)m is moved to point B(6,3,1)m. Find the work done by the force. 56. How many equations of equilibrium are defined for a concurrent force system and coplanar force system? 57. A force F = 700i + 1500j is applied to a bolt A. Determine the magnitude o ...

... 55. A force (10i + 20j – 5k) N applied at A (3,0,2)m is moved to point B(6,3,1)m. Find the work done by the force. 56. How many equations of equilibrium are defined for a concurrent force system and coplanar force system? 57. A force F = 700i + 1500j is applied to a bolt A. Determine the magnitude o ...

Electric polarization properties of single bacteria measured with electrostatic force microscopy

... the case of a solid oblate spheroid of dielectric constant r = 6.3, height D = 39 nm and eccentricities e = 1, 2, 5, 10 and 30 (for e > 30 the curves overlap). The tip radius is R = 5 nm. For all eccentricities considered the contrast decays with increasing tip–nanoparticle distance, as e ...

... the case of a solid oblate spheroid of dielectric constant r = 6.3, height D = 39 nm and eccentricities e = 1, 2, 5, 10 and 30 (for e > 30 the curves overlap). The tip radius is R = 5 nm. For all eccentricities considered the contrast decays with increasing tip–nanoparticle distance, as e ...

MU08-CHAPTER1.doc

... that question never will get any final answer, who, know. Hence, entities on that very elementary level of matter will not interact by gravitation, electrical or magnetic fields or other forms of known interaction processes. Not either these entities will show up properties of mass inertia forces. A ...

... that question never will get any final answer, who, know. Hence, entities on that very elementary level of matter will not interact by gravitation, electrical or magnetic fields or other forms of known interaction processes. Not either these entities will show up properties of mass inertia forces. A ...

Physics, Chatper 24: Potential - [email protected] of

... In the above discussion we have used the term potential at a point, while the definition was in terms of the difference of potential between two points. The term "potential at a point" can have meaning if we decide upon some reference point as a point of zero potential. In practical work this refere ...

... In the above discussion we have used the term potential at a point, while the definition was in terms of the difference of potential between two points. The term "potential at a point" can have meaning if we decide upon some reference point as a point of zero potential. In practical work this refere ...

GE6253-Engineering Mechanics - Valliammai Engineering College

... 9. Two smooth circular cylinders each of weight 1000 N and radius 15 cm are connected at their centers by a string AB of length 40 cm and rest upon a horizontal plane, supporting above them a third cylinder of weight 2000 N and radius 15 cm as shown in Figure. Predict the force S in the string AB an ...

... 9. Two smooth circular cylinders each of weight 1000 N and radius 15 cm are connected at their centers by a string AB of length 40 cm and rest upon a horizontal plane, supporting above them a third cylinder of weight 2000 N and radius 15 cm as shown in Figure. Predict the force S in the string AB an ...

# Roche limit

The Roche limit (pronounced /ʁoʃ/ in IPA, similar to the sound of rosh), sometimes referred to as the Roche radius, is the distance within which a celestial body, held together only by its own gravity, will disintegrate due to a second celestial body's tidal forces exceeding the first body's gravitational self-attraction. Inside the Roche limit, orbiting material disperses and forms rings whereas outside the limit material tends to coalesce. The term is named after Édouard Roche, who is the French astronomer who first calculated this theoretical limit in 1848.