Acylinder with rotational inertia i1 = 3.0 kg · m2 rotates clockwise about a vertical axis through its center with angular speed ω1 = 5.4 rad/s. a second cylinder with rotational inertia i2 = 1.3 kg · m2 rotates counterclockwise about the same axis with angular speed ω2 = 6.4 rad/s. if the cylinders couple so they have the same rotational axis, what is the angular speed of the combination (in rad/s)?

In a heat engine if 1000 j of heat enters the system the piston does 500 j of work, what is the final internal energy of the system if the initial energy was 2000 j ?

Total solidification times of three casting geometries are to be compared: a sphere, a cylinder, in which the length-to-diameter ration - 1.0, and a cube. volume = 1000 cm^3 for all three shhapes, and the same casting alloy is used. a) determine the solidification times of each geometry b) based on the results of part (a), which geometric element would make the best riser? c) if the mold constant = 3.5 min/cm^2 in chvorinov's rule, compute the total solidification time for each casting.

Can anybody me with this? ? (picture included.)