There is pulley which has a mass hanging from one side, and a rotating rod attached horizontally to the other (both by cables). The pulley has mass; Mp = 9.5kg and radius; Rp =0.2m. The block(A) has mass; Ma=10.9kg. The rod is L = 0.8m long and has mass=Ml7.9kg. The rod is also rotating at w= 2.7 rad/s in the anti clockwise direction. The value for gravity used is g= 9.8m/s/s downwards. Tensions are denoted by Ta and Tb
Newtons 2nd Law(F=ma), Eulers Equation (M=I[itex]\alpha[/itex]).
The Attempt at a Solution
I have defined my coordinate system as anticlockwise is positive and vertically down is positive.
Ipulley = 0.5MR2
Irod at centre of grav =(1/12)ML2
I have developed some simultaneous equations for the system:
Ta - Mag = Maaa From Newton 2nd Law of Block(A)
aa = Rp[itex]\alpha[/itex]p Acceleration relationship
-TaRp+TbRp=Ip[itex]\alpha[/itex]p Eulers equation for pulley
Tb - Mrg = Mrar Newtons second law on rod.
I also have the following(which i think is where the problem is at):
-TbL - Ir[itex]\alpha[/itex]r = -Lw2 Eulers equation on the rod at the centre of gravity.
ar = -L[itex]\alpha[/itex]r
I solved this system, and got an incorrect answer. As above i think the problem lies in the last two equations.