Vibrations and Rotations Flashcards
what is the most simple approximation of a bond
a spring with a mass at each end
letter for frequency
v
what is mu in equation for frequency of vibration
reduced mass of the system
m1 x m2 / m1 + m2
equation for reduced mass of a system
m1 x m2 / m1 + m2
affect on reduced mass of a system equation when one mass is much bigger than the other one
m1 + m2 is basically the same as m1 if thats bigger so
m1 x m2 / m1 = m2 so only the mass of the smaller one matters
which particle vibrates when one is much larger than the other
only the smaller one oscillates
application of bond vibration theory
UV spectra
what force causes the curved trajectory of pendulum
tension of a wire
equation for downwards force on pendulum
Fw = mg
define simple harmonic motion
periodic motion under the effect a restoring force
what is the period of rotation
time for one revolution
define frequency
number of revolutions per second
what is the unit of frequency
Hz (s^-1)
equation for frequency
1/T
applications of theory of pendulum
orbit around the sun
orbit of electrons in an electronic or magnetic field or electrostatic force
what is tangential velocity on a curve
velocity at the edge of the disk
equation for magnitude of velocity in constant rotation simple
v = 2piR / T
T is period of rotation
R is radius
why use angular velocity equation
doesn’t use the radius so more general
starting equations for average angular velocity
delta x / delta t x is displacement between start and end r delta theta / delta t r is radius theta angle of movement
equation for angular velocity
delta theta / delta t
what equation can the equation for angular velocity be substituted into
the second average velocity
one to get v = r w
letter for angular velocity
w
equation for kinetic energy
Ek = 1/2 m v^2
equation for energy of a particle and how you got there
Ek = 1/2 m v^2 is equation for kinetic energy
then subtitute v with v = r w equation to get
Ek = 1/2 m r^2 w^2
equation for moment of inertia around the axis of rotation
I = mr^2
substitute into Ek = 1/2 m r^2 w^2 to get
Ek = 1/2 I w^2
what is rigid body rotation
two particles with a rigid bond rotating around a pivot point
how to work out the total kinetic energy for both particles in a rigid bond
work it out individually and add them together where the two angular velocities can add wCl + wH = wHCl
application of rotational theory
in rotational-vibrational spectra finding isotopic mixtures
what is radius in a homonuclear atom
half the bond distance
what is mass 1 equal to in a homonuclear atom
mass 2
equation for moment of inertia around a point for homonuclear atoms H2
1/2 mH (dH2)^2
