classical mechanics 3e by herbert goldstein soluti
Geschreven voor
Classical mechanics 3e by herbert goldstein soluti
Classical mechanics 3e by herbert goldstein soluti
Classical mechanics 3e by herbert goldstein soluti
Alle documenten voor dit vak (17)
Verkoper
Volgen
kareey2023
Voorbeeld van de inhoud
Classical mechanics 3e by herbert goldstein solution
manual, Exercises for Physics LATEST2023
GRADED A+
Classical mechanics 3e by herbert
goldstein solution manual
Physics
Riphah International Univeristy (RIU)
149 pag.
Document shared on https://www.docsity.com/en/classical-mechanics-3e-by-herbert-goldstein-solution-manual/773867/
Downloaded by: winnie-mumbi-1 (kareey2023@gmail.com)
,Classical mechanics 3e by herbert goldstein solution
manual, Exercises for Physics LATEST2023
GRADED A+
Goldstein Classical Mechanics Notes
Michael Good
May 30, 2004
1 Chapter 1: Elementary Principles
Mechanics of a Single Particle
Classical mechanics incorporates special relativity. ‘Classical’ refers to the con-
tradistinction to ‘quantum’ mechanics.
Velocity:
dr
v= .
dt
Linear momentum:
p = mv.
Force:
dp
. F=
dt
In most cases, mass is constant and force is simplified:
d dv
F= (mv) = m = ma.
dt dt
Acceleration:
d2r
. a=
dt2
Newton’s second law of motion holds in a reference frame that is inertial or
Galilean.
Angular Momentum:
L = r ×p.
Torque:
T = r ×F.
Torque is the time derivative of angular momentum:
1
Document shared on https://www.docsity.com/en/classical-mechanics-3e-by-herbert-goldstein-solution-manual/773867/
Downloaded by: winnie-mumbi-1 (kareey2023@gmail.com)
,Classical mechanics 3e by herbert goldstein solution
manual, Exercises for Physics LATEST2023
GRADED A+
dL
T= .
dt
Work:
∫ 2
W12 = F · dr.
1
In most cases, mass is constant and work simplifies to:
∫ 2 ∫2 ∫2
dv dv
W12 = m · vdt = m v· dt = m v · dv
1 dt dt
m 2 12 1
W = (v − v ) = T − T
12 1 2 1
2 2
Kinetic Energy:
mv2
T =
2
The work is the change in kinetic energy.
A force is considered conservative if the work is the same for any physically
possible path. Independence of W12 on the particular path implies that the
work done around a closed ciruit is zero:
I
F · dr = 0
If friction is present, a system is non-conservative.
Potential Energy:
F = −∇V (r).
The capacity to do work that a body or system has by viture of is position
is called its potential energy. V above is the potential energy. To express work
in a way that is independent of the path taken, a change in a quantity that
depends on only the end points is needed. This quantity is potential energy.
Work is now V1 − V2. The change is -V.
Energy Conservation Theorem for a Particle: If forces acting on a particle
are conservative, then the total energy of the particle, T + V, is conserved.
The Conservation Theorem for the Linear Momentum of a Particle states
that linear momentum, p, is conserved if the total force F, is zero.
The Conservation Theorem for the Angular Momentum of a Particle states
that angular momentum, L, is conserved if the total torque T, is zero.
2
Document shared on https://www.docsity.com/en/classical-mechanics-3e-by-herbert-goldstein-solution-manual/773867/
Downloaded by: winnie-mumbi-1 (kareey2023@gmail.com)
, Classical mechanics 3e by herbert goldstein solution
manual, Exercises for Physics LATEST2023
GRADED A+
Mechanics of Many Particles
Newton’s third law of motion, equal and opposite forces, does not hold for all
forces. It is called the weak law of action and reaction.
Center of mass:
Σ Σ
miri miri
R= Σ = .
mi M
Center of mass moves as if the total external force were acting on the entire
mass of the system concentrated at the center of mass. Internal forces that obey
Newton’s third law, have no effect on the motion of the center of mass.
d2R Σ
F(e) ≡ M = F(e)
i .
dt2 i
Motion of center of mass is unaffected. This is how rockets work in space.
Total linear momentum:
Σ dri dR
P= mi =M .
dt dt
i
Conservation Theorem for the Linear Momentum of a System of Particles:
If the total external force is zero, the total linear momentum is conserved.
The strong law of action and reaction is the condition that the internal forces
between two particles, in addition to being equal and opposite, also lie along
the line joining the particles. Then the time derivative of angular momentum
is the total external torque:
dL
= N(e).
dt
Torque is also called the moment of the external force about the given point.
Conservation Theorem for Total Angular Momentum: L is constant in time
if the applied torque is zero.
Linear Momentum Conservation requires weak law of action and reaction.
Angular Momentum Conservation requires strong law of action and reaction.
Total Angular Momentum:
Σ Σ ′
L= ri ×pi = R ×M v + r ×p′ .
i i
i i
3
Document shared on https://www.docsity.com/en/classical-mechanics-3e-by-herbert-goldstein-solution-manual/773867/
Downloaded by: winnie-mumbi-1 (kareey2023@gmail.com)
Voordelen van het kopen van samenvattingen bij Stuvia op een rij:
√ Verzekerd van kwaliteit door reviews
Stuvia-klanten hebben meer dan 700.000 samenvattingen beoordeeld. Zo weet je zeker dat je de beste documenten koopt!
Snel en makkelijk kopen
Je betaalt supersnel en eenmalig met iDeal, Bancontact of creditcard voor de samenvatting. Zonder lidmaatschap.
Focus op de essentie
Samenvattingen worden geschreven voor en door anderen. Daarom zijn de samenvattingen altijd betrouwbaar en actueel. Zo kom je snel tot de kern!
Veelgestelde vragen
Wat krijg ik als ik dit document koop?
Je krijgt een PDF, die direct beschikbaar is na je aankoop. Het gekochte document is altijd, overal en oneindig toegankelijk via je profiel.
Tevredenheidsgarantie: hoe werkt dat?
Onze tevredenheidsgarantie zorgt ervoor dat je altijd een studiedocument vindt dat goed bij je past. Je vult een formulier in en onze klantenservice regelt de rest.
Van wie koop ik deze samenvatting?
Stuvia is een marktplaats, je koop dit document dus niet van ons, maar van verkoper kareey2023. Stuvia faciliteert de betaling aan de verkoper.
Zit ik meteen vast aan een abonnement?
Nee, je koopt alleen deze samenvatting voor $17.99. Je zit daarna nergens aan vast.
