Ongoing classical mechanics Billy Cole

Question 0

what is the formula for Kinetic Energy in linear motion? T

Answer 0

T = 0.5m||ṽ||

Question 1

define a particle.

Answer 1

a point mass. the mass is always fixed and positive

Question 2

what is the formula for velocity?

Answer 2

ṽ = ṙ(t)

= d/dt( ṟ(t) )

Question 3

what is the formula for momentum in linear motion?

Answer 3

p = mv 
momentum= mass x velocity(vector)

Question 4

what is the formula for angular momentum? about the origin

Answer 4

L = r x p
= position(vector) cross with momentum
=mr(vector) x ṙ

Question 5

what is the right hand rule? use angular momentum as an example

Answer 5

r= pointer finger
p= middle finger
r x p = thumb. always perpendicular to the other two

Question 6

what is the angular momentum formula about point O’

Answer 6

L’ = O’P x p

Question 7

what is the formula for angular momentum about an axis ⍳ ?

Answer 7

u is a unit vector in direction of ⍳. then.
L_⍳ = r x p●u
= L●u

Question 8

what are Newtons

three laws of motion?

Answer 8

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

Question 9

what is the formula for torque about the origin

Answer 9

N = d/dt( L ) 
N = r x F

Question 10

what is the formula for acceleration?

Answer 10

a = d^2/dt^2 ( r(t) )

Question 11

in circular motion, what is the angular speed? about the origin

Answer 11

ω = v/r

Question 12

what is angular velocity?

Answer 12

the vector form of angular speed, ω.

works such that v = ω x r

Question 13

what is the formula for angular momentum, using the angular velocity ?

Answer 13

L = Iω where I equals the moment of inertia.

Question 14

what is the formula of kinetic energy, using angular velocity?

Answer 14

T = 0.5Iω^2

where I equals the moment of inertia

Question 15

can you write down the summary table for linear and circular motion?

Answer 15

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Question 17

what is the degrees of freedom on a configuration space ?

Answer 17

the number of coordinates needed to describe the configuration of a system

Question 18

how is the velocity of a system of particles represented ?

Answer 18

vector q = (r_11, r_12, r_13, r_21, r_22, r_23, ….r_n1, r_n2, r_n3)

Question 19

what is the strong law of action and reaction

Answer 19

newtons third law coupled with the force between two particles is dircted along the line between them

Question 20

what do kinetic energy, momentum and angular momentum have in common?

Answer 20

they are all additive quantities.

Question 21

state the total kinetic energy of a system of particles

Answer 21

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Question 22

state the total momentum of a system particles

Answer 22

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Question 23

state the total angular momentum of a system of particles

Answer 23

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Question 24

define the centre of mass of a system of particles.

Answer 24

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Question 25

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?

Answer 25

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Question 26

what does an isolated system of particles mean

Answer 26

there is no external forces acting on the particles

Question 27

in an isolated system how does the centre of mass move. and what happens to the total momentum and angular momentum

Answer 27

the centre of mass moves with uniform velocity. and the total momentum and angular momentum are conserved

Question 28

what is the total mass of a continua ?

Answer 28

M = ∫ρdV in 3D
∫ρdA in 2D
∫ρdL in 1D

Question 29

what is the position vector of the centre of mass of a continua

Answer 29

1/M ∑ m_ir_i goes to r = 1/M∫rdm

Question 30

what is the kinetic energy of a continua ?

Answer 30

1/2∫||v||^2dm

Question 31

what is the total momentum of a continua?

Answer 31

p=∫vdm

Question 32

what is the total moment of inertia of a continua?

Answer 32

I = ∫r^2dm = ∫ρr^2dV

Question 33

define a force field.

Answer 33

if the force on a particle depends only on its position vector, then the particle is subject to a force field

Question 34

force field F is conservative if?

Answer 34

there is a function V satisfying F = -gradV

Question 35

what is the potential energy of a force field?

Answer 35

V, when force field F = -gradV.

Question 36

what is a system of conservative forces?

Answer 36

??

Question 37

what is the total energy of a conservative system ?

Answer 37

the sum of its potential and kinetic energies. E = T +V

Question 38

thm 1.10. conservation of energy?

Answer 38

In a conservative system, the total energy E does not change in time.

Question 39

A system is conservative iff?

Answer 39

A system is conservative iff the work done by moving

from state A to state B is independent of the path taken.