Problem $7\mathrm{.}98$ I

The disk A rolls without slipping on a horizontal surface. End $B$ of bar $BC$ is pinned to the edge of the disk $A,$ and end $C$ of the bar $BC$ can slide freely along the horizontal surface. In addition, bar $BC$ is pushed by the force $P=mg$ at its left end. The mass of bar $BC$ is $m_{BC},$ and the mass of the disk $A$ is $m_A.$ The system is initially at rest.

Determine the acceleration of the center of the diskA and the angular acceleration of bar $BC$ immediately after the force $P$ is applied if $m_A=m_{BC}=m.$