General Physical Pendulum Suppose we have some arbitrarily shaped solid of mass M hung on a fixed axis, that we know where the cm is located and what the moment of inertia I about the axis is Z-aXIs The torque about the rotation(z) axis for small e is(sin0≈0) d20 T=-Mgd≈-MgR MgRe=/ at e CM d20 o 0 where IgR 0=θcos(ot+d Physics 121: Lecture 22, Pg 8Physics 121: Lecture 22, Pg 8 General Physical Pendulum Suppose we have some arbitrarily shaped solid of mass M hung on a fixed axis, that we know where the CM is located and what the moment of inertia I about the axis is. The torque about the rotation (z) axis for small  is (sin   )  = -Mgd -MgR  d Mg z-axis R xCM d dt 2 2  2 = −   = MgR I where  = 0 cos(t + ) 2 2 dt d MgR I  −  =  a  