Ongoing classical mechanics Billy Cole Flashcards
what is the formula for Kinetic Energy in linear motion? T
T = 0.5m||ṽ||
define a particle.
a point mass. the mass is always fixed and positive
what is the formula for velocity?
ṽ = ṙ(t)
= d/dt( ṟ(t) )
what is the formula for momentum in linear motion?
p = mv momentum= mass x velocity(vector)
what is the formula for angular momentum? about the origin
L = r x p
= position(vector) cross with momentum
=mr(vector) x ṙ
what is the right hand rule? use angular momentum as an example
r= pointer finger
p= middle finger
r x p = thumb. always perpendicular to the other two
what is the angular momentum formula about point O’
L’ = O’P x p
what is the formula for angular momentum about an axis ⍳ ?
u is a unit vector in direction of ⍳. then.
L_⍳ = r x p●u
= L●u
what are Newtons
three laws of motion?
every body continues in a uniform state unless acted apon by an external force
F=ma or F=ṗ
every action has an equal and opposite reaction
what is the formula for torque about the origin
N = d/dt( L ) N = r x F
what is the formula for acceleration?
a = d^2/dt^2 ( r(t) )
in circular motion, what is the angular speed? about the origin
ω = v/r
what is angular velocity?
the vector form of angular speed, ω.
works such that v = ω x r
what is the formula for angular momentum, using the angular velocity ?
L = Iω where I equals the moment of inertia.
what is the formula of kinetic energy, using angular velocity?
T = 0.5Iω^2
where I equals the moment of inertia
can you write down the summary table for linear and circular motion?
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what is the degrees of freedom on a configuration space ?
the number of coordinates needed to describe the configuration of a system
how is the velocity of a system of particles represented ?
vector q = (r_11, r_12, r_13, r_21, r_22, r_23, ….r_n1, r_n2, r_n3)
what is the strong law of action and reaction
newtons third law coupled with the force between two particles is dircted along the line between them
what do kinetic energy, momentum and angular momentum have in common?
they are all additive quantities.
state the total kinetic energy of a system of particles
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state the total momentum of a system particles
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state the total angular momentum of a system of particles
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define the centre of mass of a system of particles.
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consider a set of interacting particles in euclidean space E subject to external forces.
what is the total momentum?
what is the centre of mass?
what is the total external torque?
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what does an isolated system of particles mean
there is no external forces acting on the particles
in an isolated system how does the centre of mass move. and what happens to the total momentum and angular momentum
the centre of mass moves with uniform velocity. and the total momentum and angular momentum are conserved
what is the total mass of a continua ?
M = ∫ρdV in 3D
∫ρdA in 2D
∫ρdL in 1D
what is the position vector of the centre of mass of a continua
1/M ∑ m_ir_i goes to r = 1/M∫rdm
what is the kinetic energy of a continua ?
1/2∫||v||^2dm
what is the total momentum of a continua?
p=∫vdm
what is the total moment of inertia of a continua?
I = ∫r^2dm = ∫ρr^2dV
define a force field.
if the force on a particle depends only on its position vector, then the particle is subject to a force field
force field F is conservative if?
there is a function V satisfying F = -gradV
what is the potential energy of a force field?
V, when force field F = -gradV.
what is a system of conservative forces?
??
what is the total energy of a conservative system ?
the sum of its potential and kinetic energies. E = T +V
thm 1.10. conservation of energy?
In a conservative system, the total energy E does not change in time.
A system is conservative iff?
A system is conservative iff the work done by moving
from state A to state B is independent of the path taken.
