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consider 5 independent magnetic moments. each moment has only two directions +m and -m . hamiltonian of such system is given by x = mi . if the total magnetization of the system is equal to m , the entropy is equal to
A copper wire of length 3m is subjected to a force of 5N. Calculate the elongation produced if the young’s modulus of copper is 12X1010 N/m2, if the area of cross-section of the wire is 0.785X10-6m
Find the (a) amplitude, (b) angular frequency, (c) frequency, (d) wavelength, (e) period, (f) speed of the wave, and the (g) transverse displacement at x = 0.5m and t = 2s on the following wave functions:

1.) y(x,t) = (2.5m)sin[(20 rad/m)x + (180 rad/s)t]

2.) y(x,t) = (0.35m)cos[910 rad/m)x - (120 rad/s)t]

3.) y(x,t) = (0.6m)sin[(30 rad/m)x + (90 rad/s)t]
A vertical spring has a force constant of 125N/m. By how much will the spring be compressed if a mass of 0.525kg placed on top of it?
A physics teacher sits on a rotating stool to demonstrate the conversion of angular motion. with her arms stretched, she rotates at 0.75 rev/s. When teacher's arms are tucked in close in her chest, she rotates at 1.50 rev/s. What is the ratio of her moment of inertia with outstretched arms to the moment of inertia with arms tucked in to her chest?
A motor exerts torque on a carousel for it to attain a speed of 2.5 rev/s starting from rest in 3.5s. Find the work done by the motor if the carousel has a radius of 27m and mass of 1.75 x 10^5 kg. Consider the carousel to be a thin-walled cylinder rotating about its center.
A yo-yo is a solid cylindrical-shaped object wrapped by a string. if the yo-yo has a mass of 0.020kg and a radius of 10cm, find its speed when the string is unwound, moving downward at a distance of 1.0m. The unwinding of the string took place without slipping.
What is the rotational kinetic energy of a 1.20-kg sphere with a radius of 0.250m rotating about its axis and an angular speed of 0.38 rad/s?
What angle did the tire rotate after 1 second if a spot of paint on the tire moves in a circular path with radius 0.43m while the tire move at 1.48m/s?
It takes 365.25 days for the earth to complete one revolution around the sun. Calculate the:
a.) period
b.) frequency
c.) angular frequency of the earth as it revolves around the sun
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