Bullet construct/composition have nothing to do with it. The required information is velocity and length of the projectile in multiples of its diameter (calibers). Along with the rate of twist, this will give you the angular velocity in RPM (revolutions per minute). The Greenhill formula will tell you how fast you need to spin a projectile of a given length (in calibers) to stabilize it. Weight does not come into the calculation. People mention weight because cup and core bullets of a certain design get longer as they get heavier, but just because they are longer does not mean they are heavier.
If this sounds confusing, think of a boattail hollowpoint VLD profile bullet compared to a round nose flat base bullet of the same weight traveling at the same velocity. The boattail hollow point bullet will be longer than a flat base round nose bullet, and would require a faster twist to stabilize it.
Realize also that manufacturers typically put barrels on rifles that will stabilize the heaviest bullet commercially available for that rifle, so a 1:10" twist barrel on a 30-06 will properly stabilize a 220 gr flat point spitzer bullet. The USMC M40A1 and A3 sniper rifles have a 1:11" twist to stabilize 168 gr and 172 gr bullets used in those rifles.