Newtonian Dynamics

Question 1

dimensional analysis

Answer 1

write out variables with exponents of alpha, beta, gamma

plug in dimesions

make LHS and RHS compatible

Question 2

kinematics

Answer 2

studies how the motion takes place and describes its geometrical features

Question 3

dynamics

Answer 3

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

Question 4

x in polar coords

Answer 4

rsin theta cos phi

Question 5

y in polar coords

Answer 5

rsin theta sin phi

Question 6

z in polar coords

Answer 6

rcos theta

Question 7

trajectory

Answer 7

set of points traced by the particle during its motion

Question 8

xt diagram

Answer 8

time on x axis
position on y axis

Question 9

uniform motion

Answer 9

zero acceleration

Question 10

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

Answer 10

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

use dimensional analysis to work out k

Question 11

2 dimensions
x=

Answer 11

rcos theta

Question 12

2 dimensions
y=

Answer 12

rsin theta

Question 13

curvilinear coordinate

Answer 13

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

Question 14

velocity of particle in vectorial form

Answer 14

v=ds/dt ut = vut

where ur is the unit vector tangent to the trajectory

Question 15

relation between cartesian and polar unit vectors

Answer 15

ur=costheta ux + sintheta uy

utheta = -sintheta ux + costheta uy

Question 16

equation for trajectory of particle is obtained by

Answer 16

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

Question 17

range

Answer 17

maximum distance xr travelled by the particle

Question 18

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

Answer 18

vectorial equation

r=r0’+r’

Question 19

poisson formula

Answer 19

db/dt=wxb

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

Question 20

dux/dt=

Answer 20

wxux

(same for y and z)

Question 21

relative motion: v=

Answer 21

v’+v0’+wxr’

Question 22

centrifugal acceleration

Answer 22

ac=-wx(wxR) directed outwards

Question 23

coriolis acceleration

Answer 23

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

responsible for cyclones etc

Question 24

first law - principle of inertia

Answer 24

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

Question 25

inertial reference frame

Answer 25

non accelerating

Question 26

second law

Answer 26

F=ma

Question 27

inertial mass

Answer 27

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

Question 28

F=ma cartesian differential equation

Answer 28

ma=m d2r/dt2

Question 29

newton's equation is only valid in

Answer 29

intertial reference frames and in the non-relativistic limit

Question 30

third law

Answer 30

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

Question 31

p=mv so F=

Answer 31

dp/dt *also valid when mass is not constant*

Question 32

impulse

Answer 32

J = integral of F dt variation of the momentum in a time interval in the case of constant mass J=m delta v

Question 33

F=ma in non-inertial reference frame

Answer 33

additional terms appear such as centrifugal and coriolis forces

Question 34

microscopically, contact forces originate from

Answer 34

electrostatic interactions between electric charges

Question 35

ideal string

Answer 35

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

Question 36

difference between rods and strings

Answer 36

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

Question 37

drag forces are experienced by

Answer 37

bodies moving in fluids type of frictional force, ie always in opposite direction Fdrag=-bv

Question 38

work done

Answer 38

W= integralF.ds

Question 39

power

Answer 39

dW/dt P=F.ds/dt = F.v

Question 40

conservative forces

Answer 40

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

Question 41

examples of conservative forces

Answer 41

weight elastic forces

Question 42

examples of a non-conservative force

Answer 42

friction

Question 43

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

Answer 43

in the presence of conservative forces only

Question 44

mechanical energy

Answer 44

Ek+Ep

Question 45

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

Answer 45

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

Question 46

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

Answer 46

LO = r × p = r × mv.

Question 47

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

Answer 47

LO′ = LO + O′O × mv where O'O is the vector from O to O'

Question 48

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

Answer 48

MO = r × F

Question 49

the statement of the theorem of the angular momentum

Answer 49

dLO/dt = r × ma = r × F = MO.

Question 50

central force

Answer 50

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

Question 51

gravitational potential energy

Answer 51

Ep=-Gm1m2/r

Question 52

gravitational potential generated by a mass M

Answer 52

V(r)=-GM/r

Question 53

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

Answer 53

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

Question 54

theorem of the centre of mass

Answer 54

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

Question 55

reference frame of the CM is identified by the properties:

Answer 55

its origin in the CM of the system its axes do not rotate and are parallel to the axes of an inertial reference frame

Question 56

König’s theorems

Answer 56

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.

Question 57

first koing theorem

Answer 57

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.

Question 58

second konig theorem

Answer 58

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.

Question 59

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

Answer 59

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.

Question 60

The general motion of an extended (rigid) body is

Answer 60

a roto-translation (composition of a translation and a rotation)