T - IfB

Degrees of freedomIn two dimensions ω is always directed orthogonalto the plane and therefore can be considered to be ascalar. One angle is therefore enough to describe allrotations. One consequently has three degrees offreedom: 2 translational and 1 rotational.In three dimensions ω is a three dimensionalvector and one needs three correspondinggeneralized coordinates (angles), so one has sixdegrees of freedom: 3 translational and 3 rotational.75Two dimensionsf t2I r ()r dA• rI TAmoment of inertiacenter of massTAf () r rdAttorqueequation of motion for rotation :76