Consider an aqueous solution of N = 1022 dye molecules separated from pure solvent by a movable, semipermeable plug: Lmax In class we estimated the probability distribution P(L) x (L) for finding the plug at a distance L from the top of the solution, where 2(L) x LN is the number of ways available space above the plug. arrange N solutes in the If no external force is applied to the plug, we argued, the maximum value of P(L) should occur when L takes on its largest possible value, Lmax. Here you will estimate the size of typical fluctuations in plug position, AL Lmax - L. (a) What displacement ALtyp gives a probability (per unit length) equal to ten percent of the max- imum? In other words, solve the equation P(Lmax - ALıyp) = 0.1P(Lmax). For this purpose use a Taylor expansion of In 2 around Lmax To determine a numerical value for ALtyp, take the container's height to be Lmax = 10 cm. (b) Thermodynamics concerns the behavior of average macroscopic quantities, such as the length L in our dye solution, and neglects fluctuations about mean values. Comment on the validity of this approach in light of your answer to part (a).

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Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.