Coriolis Effect on Missiles
Coriolis force on the
missile
a c 2 v sin v
(Taking 300 )
For a cruise missile fired at a target
distant L away, the deviation S is :
1 2 1 L2
s act
2
2 v
For L 10 km, v 700 m / s, 7.0 105 rad / s
s 5m
Outside Inertial
observe
MEchanics Oscillations and
Waves (MEOW)
D. D. Pant
Associate Professor
Department of Physics
BITS Pilani, Pilani
E-Mail: ddpant@pilani.bits-pilani.ac.in
Office: 3242-L
Major Division
1. Mechanics : 20 Lectures
2. Oscillations & Waves : 20 Lectures
Textboo
BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, Pilani
Pilani Campus
INSTRUCTION DIVISION
SECOND SEMESTER 2014 -2015
Course Handout (Part-II)
Date: 12/01/2015
In addition to part I (General handout for all courses appended to the timetable) this portion
gives
Chapter IV
Forced/Driven Oscillations
An additional externally applied harmonic
force acts on the oscillator
Without Damping
d2x
m 2 k x F0 cos t
dt
Or,
d2x
F0
2
0 x cos t
2
dt
m
0 : Natural angular frequency
: Angular frequency of driving force
Ex1. Sp
Chapter V
Coupled Oscillators
and Normal Modes
Two, or more, oscillators coupled together
Examples
1. Two pendulums, coupled by a spring
2. A molecule
CO2 Molecule
3. A crystalline solid
4. An elastic medium, like a vibrating string
Two Simple Pendulums C
MEchanics Oscillations and
Waves (MEOW!)
RISHIKESH
VAIDYA
Ph.D.(Theoretical Particle Physics)
Oce: 3265
rishidilip@gmail.com
Physics Group, B I T S
August 2, 2011
Pilani
A Simple Quiz
What is the shape of liquid?
A Simple Quiz
What is the shape of liquid?
R.R. Mishra
Department of Physics
Chapter No. 8
Motion in Noninertial
Frames
Motion Looks Different From Different
Frames
Football kicked into the air
Man on the Ground
Man on a Parachute
Bungee Jumper
A reference frame is a rigid body with
three referenc
Chapter IV
Forced/Driven
Oscillations
An additional externally applied harmonic
force acts on the oscillator
Without Damping
d2x
m 2 k x F0 cos t
dt
Or,
d2x
F0
2
0 x cos t
2
dt
m
0 : Natural angular frequency
: Angular frequency of driving force
Example
Rotating Coordinate System
z
z
(x,y,z) : Inertial frame
y
(x,y,z) : Frame rotating w.r.t
the inertial frame
y
x
x
Goal : Find the equation of motion of a
particle in frame (x,y,z)
Result I
Change in a vector that undergoes infinitesimal
rotation about a f
Chapter IV
Forced/Driven Oscillations
An additional externally applied harmonic
force acts on the oscillator
Without Damping
d 2x
m 2 k x F0 cos t
dt
Or,
d2x
F0
2
0 x cos t
2
dt
m
0 : Natural angular frequency
: Angular frequency of driving force
Ex1. S
Chapter 3
1. Dynamics of a System of Particles &
Conservation of Momentum
2. Centre of Mass & its Motion
3. Centre of Mass coordinates
4. Motion of Systems with Variable Mass
5. Momentum Transport
Dynamics of a System of Particles
fj
dp j
dt
int ext
f j
Chapter No. 8
Motion in Noninertial
Frames
Motion Looks Different From Different
Frames
Football kicked into the air
Man on the Ground
Man on a Parachute
Bungee Jumper
A reference frame is a rigid body with
three rigid axes attached to it
v
z
r
a
y
x
Are
Chapter 7
Progressive
Waves
Waves
Types of Waves
Mathematical description of Waves
Three Velocities in Wave Motion
WAVE MOTION
Motion of infinite coupled oscillators
Transport of Energy without transport of matter
What is a Wave?
Key word - Disturbance
Problem 6.40 and 6.41 Kleppner and Kolenkow
Notes by: Rishikesh Vaidya, Physics Group, BITS-Pilani
6.40 A wheel with ne teeth is attached to the end of a spring with constant k and unstretched length l. For x > l, the wheel slips freely on the surface, bu
Prob. 4.7
A ring of mass M hangs
from a thread, and two
m
beads of mass m each
slide on it without
friction. The beads are
released simultaneously
M
from the top of the ring and slide
down opposite sides. Show that the
ring will start to rise if m > 3M/2,
Chapter IV
Forced/Driven Oscillations
An additional externally applied harmonic
force acts on the oscillator
Without Damping
d 2x
m 2 k x F0 cos t
dt
Or,
d2x
F0
2
0 x cos t
2
dt
m
0 : Natural angular frequency
: Angular frequency of driving force
Ex1. S
Mechanics in Noninertial Frames
Why Frames of Reference?
Newtons Equations :
d r
F = ma =m 2
dt
2
are meaningless without frame of reference,
w.r.t which, the position vector, and
consequently the acceleration vector, are
measured.
A reference frame is a
Simple Harmonic Motion
The idealized SHO is a spring-mass
system
F = -kx
Equation of
motion :
2
d x
m 2 k x
dt
O
(The equilibrium
position)
Or,
d2x
2
x 0
2
dt
k
2
m
x
The most general solution of the above equation is
:
(A & B are arbitrary
x ( t ) A
Chapter V
Coupled Oscillations
Two, or more, oscillators coupled together
Examples
1. Two pendulums, coupled by a spring
2. A molecule
CO2 Molecule
3. A crystalline solid
4. Coupled electrical oscillators
~
5. An elastic medium, like a vibrating string
A
Lectures on Oscillation and waves
By
Kusum Lata
Chamber No. 3242-K
Email Id kusum@pilani.bits-pilani.ac.in
Mobile No. 09694096462
Text Book: Vibration and Waves by A P French
Reference Book: Waves and Oscillations by N K
Bajaj
The world is full of oscilla
Chapter VI
Angular Momentum & FixedAxis Rotation
Angular Momentum
Angular Momentum of a single particle :
p
r
L=rp
o
For a system of particles :
L
Li
i
ri pi
i
Prob. 6.1
Show that if the total linear momentum
of a system of particles is zero, the
a
Chapter IV
Work & Energy
1. Work done by a force :
2. Kinetic Energy & Work-Energy Theorem
3.Conservative Forces and Potential
Energy
4. Potential Energy and Stability
5. Collision
Work done by a force
F
F
Impulse
t
Ft m(v 2 v1
Work
x
1
1
2
2
Fx mv 2 mv1
Chapter 3
Momentum
1. Dynamics of a System of Particles &
Conservation of Momentum
2. Concept of Centre of Mass
3. Motion of Systems with Variable Mass
Dynamics of a System of Particles &
Conservation of Momentum
The Two Particles System
Two masses connec
Prob. 6.13
m
Mass m is attached to
m
a post of radius R.
Initially it is at a
distance r0 from the
(b)
(a)
centre of the post and
is moving tangentially
with velocity v0. In case (a) the string passes
through a hole in the centre of the post at the
top. T
Chapter 6
Normal Modes of
Continuous System
The Free Vibrations of
Stretched Strings
Parameters of the string :
Length : L
Tension : T
Density (Linear) :
y
x
When the string vibrates, the displacement y is
a function of both x and t
At a fixed time, y is
Chapter IV
Work & Energy
1. Work done by a force : Line Integral
2. Kinetic Energy & Work-Energy Theorem
3.Conservative Forces and Potential
Energy
4. Potential Energy and Stability
Work Done by a Force
F( ri )
B
A
rA
rB
ri
O
F
W F r
r
F( ri )
ri
A
Chap. 6: Angular Momentum and Fixed
Axis Rotation
Rishikesh Vaidya
Theoretical Particle Physics
Oce: 3265
rishidilip@gmail.com
Physics Group, B I T S
Pilani
September 7, 2012
Outline
1
Introduction
2
Angular Momentum as a Pseudo (or Axial) Vecto
3
Torque