We discuss evolution of the magnetic flux density and angular velocity in a molecular cloud core , on the basis of three-dimensional numerical simulations , in which a rotating magnetized cloud fragments and collapses to form a very dense optically thick core of > 5 \times 10 ^ { 10 } { cm } ^ { -3 } .
As the density increases towards the formation of the optically thick core , the magnetic flux density and angular velocity converge towards a single relationship between the two quantities .
If the core is magnetically dominated its magnetic flux density approaches 1.5 ( n / 5 \times 10 ^ { 10 } { cm } ^ { -3 } ) ^ { 1 / 2 } mG , while if the core is rotationally dominated the angular velocity approaches 2.57 \times 10 ^ { -3 } ( n / 5 \times 10 ^ { 10 } { cm } ^ { -3 } ) ^ { 1 / 2 } yr ^ { -1 } , where n is the density of the gas .
We also find that the ratio of the angular velocity to the magnetic flux density remains nearly constant until the density exceeds 5 \times 10 ^ { 10 } { cm } ^ { -3 } .
Fragmentation of the very dense core and emergence of outflows from fragments are shown in the subsequent paper .