Problem

Body A$,$ a $30$ kg train signal, is attached to beam B of mass $150$ kg $.$ B is suspended from a rigid support by a hinge and a cable. The geometry of the system is shown at right.

a$.$ What is the tension in the cable? Be sure to include a detailed free body diagram to accompany your analysis.

b$.$ What is the magnitude of the force provided by the hinge?

c$.$ What is the moment of inertia of $\backslash (\backslash$mathrm$\{$A$\}+\backslash$mathrm$\{$B$\}\backslash )$ as a rigid system, if rotating about the hinge?

PHYS$-1600$: For analysis, break the beam into two separate beams: a short beam to the left of the hinge, and a longer beam to the right of the hinge.

PHYS$-2000$: Treat the beam as a single bar, using integral calculus without breaking it into two pieces.

d$.$ If the cable were to break, what would the angular acceleration of $\backslash (\backslash$mathrm$\{$A$\}+\backslash$mathrm$\{$B$\}\backslash )$ be at the moment of breakage? What tangential acceleration would A experience? What tangential acceleration would the end of B $($where it was previously attached to the cable$)$ experience?