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Problem $16\mathrm{.}034-$ Double pulleys initially at rest

Each of the double pulleys shown has a mass moment of inertia of $15lb*ft*s^2$ and is initially at rest. The outside radius is $18$ in $.,$ and the inner radius is $9$ in $.$ Consider, $M_1=200lb,M_2=200lb,M_3=500lb,M_4=340lb,$ and $M_5=120lb.$

$(1)$

$(2)$

$(3)$

$(4)$

Problem $16\mathrm{.}034.$a $-$ Angular acceleration of double pulleys

Determine the angular acceleration of each pulley. $($Round the final answers to three decimal places.$)$

Case $1$:

The angular acceleration of the pulley is

xra$\frac{d}{s^2}.$

Case $2$:

The angular acceleration of the pulley is

xra$\frac{d}{s^2}.$

Case $3$:

The angular acceleration of the pulley is

$ra\frac{d}{s^2}.$

Case $4$:

The angular acceleration of the pulley is

$ra\frac{d}{s^2}.$