$1)($SOLVE USING COMPONENT METHOD WITH PICTURES$)($PRACTICE EXAM QUESTION$)$ The smooth $4-$kg cylinder C in the figure below has a peg P through its center which passes through the slot in the arm $\backslash ($ O A $\backslash ).$ If the arm rotates in the vertical plane with a constant angular velocity of $\backslash (0\mathrm{.}5\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}\backslash ),$ find: a$)$ the linear velocity and acceleration of the cylinder C$,$ b$)$ normal force of the cylinder with the horizontal surface, and c$)$ the force that the arm exerts on the peg at the instant $\backslash (\backslash$Theta$=50^\{\backslash$circ$\}\backslash ).$

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