Problem S10.3. Consider a particle undergoing rotational Brownian motion. Write an expression for the angular velocity autocorrelation function for the rotating Brownian particle. Show that for long times it depends on time as follows:

where po is the fluid density, 7 is the shear viscosity, I is the moment of inertia of the sphere, and (2(0)), is the initial mean square angular velocity. (Hint: Use the result of Problem S10.2 for the friction coefficient.)

Transcribed Image Text:

Can (1) 22 Po 4nt 5/2 ((0)),