Figure 2 represents an automatic door closing mechanism, OB is a door whose length b is 1.25m, and the weight is 40kg, C is a collar with a rod passing through, the spring coefficient on the short rod is k, when 0=0 no spring deformation; if a force P=225N is applied to the cable connecting the door, and when the included angle of the door is = 60, its angular velocity is 1 rad s/ clockwise rotation, (Hint: the mass moment of inertia of the door, please refer to the value of the thin rod) < (a) Find the k of the spring (5%) < (b) When the included angle of the door 0 = 45 , what is the corresponding angular velocity? (5%) < b 0 0 20 I=mR Axis Axis Axis Axis Axis Hoop about cylinder axis Solid cylinder (or disk) about cylinder axis 1 ==R Thin rod about axis through center 1 to length m 1="p 12 2R Solid sphere about any diameter I= 2m MR Hoop about any diameter 1: === R Axis Axis Axis Axis Axis Annular cylinder (or ring) about cylinder axis 1= (R+R) Solid cylinder (or disk) about central diameter 1==R Thin rod about axis through one end to length P 1 = Thin 2R spherical shell about any diameter I=R Slab about 1 axis through center m 12