For a rigid axisymmetric satellite, the mass moment of inertia about its long axis is 1000 kg$m2 , and the moment of inertia about transverse axes through the center of mass is 5000 kg$m2 . It is spinning about the minor principal body axis in torque-free motion at 6 rad/s with the angular velocity lined up with the angular momentum vector H. Over time, the energy degrades due to internal effects and the satellite is eventually spinning about a major principal body axis with the angular velocity lined up with the angular momentum vector H. Calculate the change in rotational kinetic energy between the two states. {Ans.: 14.4 kJ}

Delta T = - 14.4 kJ

Explanation:

Firstly the initial momentum of the satellite is;

H0 = L0*W0

L0 is the momentum of inertia of the satellite about its longer axis (1000 kg.m^2) and Wo is the initial angular velocity of the satellite ( 6 rad/s)

now we substitute

H0 = 1000 kg.m^2 * 6 rad/s

H0 = 6000 kg.m^2

Now the initial rotational kinetic energy of the satellite is;

0o = 1/2L0W0^2

we substitute

T0 = 1/2 * (1000 kg.m^2) * (6 rad/s)^2

T0 = 18000

Next is the final angular momentum of the satellite;

H = IW

I is the moment of inertia of the satellite about its transverse axes through center of mass (5000 kgm^2)

we know that the law of conservation angular momentum, the total initial angular momentum of the satellite is equal to the total final angular momentum of the satellite.

simply put H = H0

we know that our H0 = 6000 kgm^2

so we substitute

H0 = IW

6000 kg.m^2 = 5000 kgm^2 * W

W = 1.2 rad/s

The final rotational kinetic energy of the satellite is;

T = 1/2IW^2

T = 1/2 * 5000 kgm^2 * 1.2^2

T = 3600 J

so the change in rotational kinetic energy of the satellite is;

Delta T = T - T0

Delta T = 3600 - 18000

DeltaT = - 14400 J

Delta T = - 14.4 kJ

answer; (d) spontaneous processes are characterized by the overall conversion of order to disorder;

explanation:

earth's surface is mainly heated by the absorption of infrared radiation from the sun.

evaporation occurs because molecules in liquid water are warmed ( usually by the sun) and vibrate quicker, becoming less dense and rise.

condensation occurs because molecules in water vapor are cooled and therefore vibrate more slowly thus becoming more dense and eventually fall to earth.

lines of equal barometric pressure on a weather map are called: isobars : lines of equal temp on a weather map are called: isotherms.​