>As per gravitation laws, the farther the star is, the slower it should rotate.
That depends. The 1/R orbital speed relationship is valid only in cases of spherically symmetric mass distribution or when the radiuses of the interacting masses being much smaller than the distance between them. Neither of these is true for a star inside a galaxy disk. Correctly accounting for the disk shape gives you expected orbital speed much closer to the "outer stars in the galaxy rotate at the same speed as inner stars", though not exactly equal. The remaining difference is explained by the seond factor.
That second factor is that "rotate" i suppose means orbiting around galaxy center. The stars in the disk aren't really orbiting, ie. they are actually flying away like in a fireworks wheel as the galaxy disk becomes larger and thinner - exactly because the stars' speed is still somewhat higher than the orbital speed as calculated above. Thus no need for DM here.
That depends. The 1/R orbital speed relationship is valid only in cases of spherically symmetric mass distribution or when the radiuses of the interacting masses being much smaller than the distance between them. Neither of these is true for a star inside a galaxy disk. Correctly accounting for the disk shape gives you expected orbital speed much closer to the "outer stars in the galaxy rotate at the same speed as inner stars", though not exactly equal. The remaining difference is explained by the seond factor.
That second factor is that "rotate" i suppose means orbiting around galaxy center. The stars in the disk aren't really orbiting, ie. they are actually flying away like in a fireworks wheel as the galaxy disk becomes larger and thinner - exactly because the stars' speed is still somewhat higher than the orbital speed as calculated above. Thus no need for DM here.