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Physics 2 > Newtonian Dynamics > Flashcards

Newtonian Dynamics Flashcards

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1
Q

dimensional analysis

A

write out variables with exponents of alpha, beta, gamma

plug in dimesions

make LHS and RHS compatible

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2
Q

kinematics

A

studies how the motion takes place and describes its geometrical features

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3
Q

dynamics

A

considers the origin of the motion and investigates the interactions between physical objects

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4
Q

x in polar coords

A

rsin theta cos phi

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5
Q

y in polar coords

A

rsin theta sin phi

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6
Q

z in polar coords

A

rcos theta

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7
Q

trajectory

A

set of points traced by the particle during its motion

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8
Q

xt diagram

A

time on x axis
position on y axis

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9
Q

uniform motion

A

zero acceleration

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10
Q

because of viscous effects, a particle moving in a fluid or a gas feels

A

an acceleration that is proportional to its velocity and opposite in direction

use dimensional analysis to work out k

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11
Q

2 dimensions
x=

A

rcos theta

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12
Q

2 dimensions
y=

A

rsin theta

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13
Q

curvilinear coordinate

A

s
identifies the location of the particle along the trajectory with respect to a certain origin

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14
Q

velocity of particle in vectorial form

A

v=ds/dt ut = vut

where ur is the unit vector tangent to the trajectory

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15
Q

relation between cartesian and polar unit vectors

A

ur=costheta ux + sintheta uy

utheta = -sintheta ux + costheta uy

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16
Q

equation for trajectory of particle is obtained by

A

eliminating the time variable from x(t) and y(t)

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17
Q

range

A

maximum distance xr travelled by the particle

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18
Q

The relation between the positions r, r’ of the particle, measured respectively by S, S′ is given by

A

vectorial equation

r=r0’+r’

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19
Q

poisson formula

A

db/dt=wxb

w is angular velocity vector whose magnitude is euqal to the angular velocity of the rotation

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20
Q

dux/dt=

A

wxux

(same for y and z)

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21
Q

relative motion: v=

A

v’+v0’+wxr’

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22
Q

centrifugal acceleration

A

ac=-wx(wxR) directed outwards

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23
Q

coriolis acceleration

A

as=-2wxv’ is orthogonal to both the angular velocity vector and the velocity v’ of the particle wrt S’

responsible for cyclones etc

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24
Q

first law - principle of inertia

A

consider a body on which no net forces act.

If the body is at rest it will remain at rest

If the body is moving with constant velocity it will continue to do so

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25
Q

inertial reference frame

A

non accelerating

26
Q

second law

A

F=ma

27
Q

inertial mass

A

mass accounts for the inertia of the body (resistance to variation in motion)

28
Q

F=ma cartesian differential equation

A

ma=m d2r/dt2

29
Q

newton’s equation is only valid in

A

intertial reference frames and in the non-relativistic limit

30
Q

third law

A

whenever two bodies A and B interact, the force Fab exerted from A on B is equal in magnitude and opposite in direction to the force Fba that B exerts on A

31
Q

p=mv so F=

A

dp/dt

also valid when mass is not constant

32
Q

impulse

A

J = integral of F dt

variation of the momentum in a time interval

in the case of constant mass J=m delta v

33
Q

F=ma in non-inertial reference frame

A

additional terms appear such as centrifugal and coriolis forces

34
Q

microscopically, contact forces originate from

A

electrostatic interactions between electric charges

35
Q

ideal string

A

non-extendable, massless string (applies to strings and rods)

36
Q

difference between rods and strings

A

string is only able to transmit tension forces, not compression forces

37
Q

drag forces are experienced by

A

bodies moving in fluids

type of frictional force, ie always in opposite direction

Fdrag=-bv

38
Q

work done

A

W= integralF.ds

39
Q

power

A

dW/dt

P=F.ds/dt = F.v

40
Q

conservative forces

A

line integral does not depend on the actual trajectory but only on initial and final positions

41
Q

examples of conservative forces

A

weight
elastic forces

42
Q

examples of a non-conservative force

A

friction

43
Q

the sum of the kinetic and potential energy is a constant only when

A

in the presence of conservative forces only

44
Q

mechanical energy

A

Ek+Ep

45
Q

in the presence on non-conservative forces, the mechanical energy is

A

not conserved and the variation is equal to the work done by the non-conservative forces

46
Q

The angular momentum LO of a particle, calculated with respect to the origin O, is
defined as

A

LO = r × p = r × mv.

47
Q

If we change the origin, the angular momentum changes accordingly as

A

LO′ = LO + O′O × mv

where O’O is the vector from O to O’

48
Q

we define the moment MO of a force, with respect to the origin
O, as

A

MO = r × F

49
Q

the statement of the theorem of the angular momentum

A

dLO/dt = r × ma = r × F = MO.

50
Q

central force

A

force that acts radially from a centre O whose magnitude is a function of the distance r=|r| from O

51
Q

gravitational potential energy

A

Ep=-Gm1m2/r

52
Q

gravitational potential generated by a mass M

A

V(r)=-GM/r

53
Q

The gravitational field generated by a system of many particles is obtained as

A

the vector sum of the contributions due to each individual particle:

54
Q

theorem of the centre of mass

A

CM of a
system of particles moves as a massive particle, with mass equal to the total mass of
the system, under a force that is given by the net external force acting on the system
itself

55
Q

reference frame of the CM is identified by the properties:

A

its origin in the CM of the system

its axes do not rotate and are parallel to the axes of an inertial reference frame

56
Q

König’s theorems

A

relate the values of L and Ek calculated in an inertial reference frame
with the corresponding quantities L′
,Ek’ calculated in the reference frame of the CM.

57
Q

first koing theorem

A

The theorem states that the angular momentum L, calculated in the inertial reference
frame, is the sum of the angular momentum L’
calculated with respect to the reference
frame of the CM and the angular momentum LCM ≡ rCM × mvCM of the center of
mass thought as a material object of mass m in the inertial reference frame.

58
Q

second konig theorem

A

The theorem states that the energy Ek of the system, calculated in the inertial reference
frame, can be expressed as the sum of the kinetic energy
of the system
with respect to the reference frame of the CM and the kinetic energy
of the CM thought as a material object of mass m in the inertial reference frame.

59
Q

König’s theorems show that both Ek and L can be decomposed as the sum of two
terms:

A
  1. A component accounting for the motion of the CM, that describes the average
    translation of the system.
  2. A component accounting for the motion of the system with respect to the CM.
60
Q

The general motion of an extended (rigid) body is

A

a roto-translation

(composition of a translation and a rotation)

61
Q
A

Physics 2 (8 decks)

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