ENES$221$

Dynamics

Group Problem $10$

A $100$ kg spool has a radius of gyration $k_G=0\mathrm{.}3m.$ A rope iswrapped several times around the inner cylinder of the spool so that when you pull horizontally on the rope it tightens on the bottom of the spool. Find the maximum acceleration of the center of the spool when pulling on the rope and the rim of the spool does not slip. The coefficient of static friction between the spool and ground is $0\mathrm{.}32.$ Note the direction that the spool moves.

$\frac{f}{N}={}_s$

Solve without instantaneous center of zero velocity

Use this for parts moving away from

$v_C=v_A+r_{\frac{C}{A}}+(v_{\frac{C}{A}}{)}_{xyz}$

$a_C=a_A+{}^{}{r}_{\frac{C}{A}}+(r_{\frac{C}{A}})+2(v_{\frac{C}{A}}{)}_{xyz}+(a_{\frac{C}{A}}{)}_{xyz}$

Use this for parts with fixed points

$v_D={}_{\frac{A}{D}}{r}_{\frac{D}{A}}$

$a_D={}_{AD}{r}_{\frac{D}{A}}-{}_{AD}^2(r_{\frac{D}{A}})$