1) Circular Motion Flashcards
Rotation of a rigid body around an axis
- all points of the body perform circular motion
- the circular trajectories lie in a parallel line
- the centre of the circle lies on the axis of rotation
Equation of circular motion
Alpha= f(t)
DRAWING
Angular velocity equation and angular acceleration equation
Angular velocity
W= d(alpha)/ dt
Angular acceleration
E= Dw/dt
Distance, velocity and acceleration
Distance travelled
S=r(alpha)
Velocity
V=rw
Acceleration
a_t=rE
DRAWING
Centripetal force
For uniform rotation of a particle with mass M a force of constant magnitude is needed pointing towards the centre or rotation = F_c
F_c changes the direction of velocity and gives rise to centripetal acceleration a_c
F_c= m x a_c
a_c= rw^2
Torque (moment)
Torque(M) exerted by F relative to the axis of rotation
M= F r sinB B= Vector between F and r
B and M can be negative or positive depending on direction of rotation
M can change the magnitude of velocity
Separation of components in heterogeneous system
Place heterogeneous system in field of appropriate force
Sedimentation
Separation of components of a heterogeneous system by gravity.
F_g=mg=pVg
F_a= p_sVg
F=(p-p_s) Vg
DRAWING
Sedimentation 2
When P = Ps the heterogeneous system can’t be separated by sedimentation
DRAWINGS
Centrifugation
Gravitational forces are weak and sedimentation only takes place very slowly or is impossible bc of diffusion (Brownian motion)
Centrifugation is the separation of the components of a heterogeneous system by the centripetal force
Centrifugation 2
DRAWING
F= (P-Ps) Va_c
F=(P-P_s) Vrw^2
Separation of components in heterogeneous system
Place heterogeneous system in field of appropriate force
Sedimentation
Separation of components of a heterogeneous system by gravity.
F_g=mg=pVg
F_a= p_sVg
F=(p-p_s) Vg
DRAWING
Sedimentation 2
When P = Ps the heterogeneous system can’t be separated by sedimentation
DRAWINGS
Centrifugation
Gravitational forces are weak and sedimentation only takes place very slowly or is impossible bc of diffusion (Brownian motion)
Centrifugation is the separation of the components of a heterogeneous system by the centripetal force
Centrifugation 2
DRAWING
F= (P-Ps) Va_c
F=(P-P_s) Vrw^2
Centrifugation 3
When p =p_s then the separation of heterogenous systems using centrifugation will not occur
DRAWING
Sedimentation rate and duration of sedimentation
All moving particles experience drag
F_d=Fv
F= friction
V= velocity
DRAWING
Sedimentation rate and duration of centrifugation 2
Particles with constant velocity:
Fv=(p-p_s)vrw^2
Terminal velocity:
V=(p-p_s)vrw^2/F
The centrifugation time is sufficient for even the most distant particles to reach the end of the tube
Sedimentation rate
This is proportional to
P-P_s
r
The square of W
The reciprocal of f
Sedimentation coefficient and relative centrifugal force RCF
Sedimentation coefficient:
S=v/a_c = v(p-p_s)/f
RCF:
G= a_c/g = rw^2/g
Centrifuge and main parts
An instrument that separates heterogenous systems by rotation
Main parts
- axis
- rotor (fixed angle rotor)
- motor (swinging bucket rotor)
Rotor balancing
The overall radial force has to be very small otherwise the centrifuge could be damaged
- ensure that tubes are placed symmetrically to distribute weight evenly
- the masses of the tubes have to be equal
Types of centrifuges
Preparative
- used for the isolation of cell membranes, organelles and cells
Analytical
-used for the investigation of biological macromolecules
Centrifugal methods
Differential centrifugation
- suspension of 2 solid fractions
Centrifugation at low speed will isolate fractions with higher sedimentation
Centrifugation at high speed will seaports second fraction from solvent
Centrifugation methods
Zone centrifugation
-mixture of 3 solid fractions
The density of solvent is growing from top to bottom
The mixture of particles is placed at the top
Centrifugation results in the grouping of particles according to sedimentation rate
Centrifugation methods
Isopycnic centrifugation
-mixture of 3 solid fractions
The sample is stirred this produces a density gradient during centrifugation
The particles move to the place where the density of the solvent is equal to their own density and stop
