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• Notes

$\begin{array}{l}{16-82 . \text { Determine the angular velocity of } \text { link } A B \text { at the }} \\ {\text { instant shown if block } C \text { is moving upward at } 12 \text { in } / \mathrm{s} \text { . }}\end{array}$

$v_{c}=12 in /s$

$\frac{4}{\sin 45}=\frac{r_{I C-B}}{\sin 30}=\frac{r_{I C-C}}{\sin \left(105^{\circ}\right)}$

$r_{I{C}-C}=5.464 \mathrm{in}$

$r_{IC-B}=2.828 \mathrm{in}$

$v=\omega r$

$v_{c}=\omega_{B c}\left(r_{IC-C}\right)$

$12=\omega_{BC}(5.464)$

$∴ \omega_{ B C}=2.1962 \mathrm{rad} / \mathrm{s}$

$V_ B=\omega_{ B C}(r_{ I C-B})$

$=2.1962(2.828)$

$=6.211 \mathrm{in} / \mathrm{s}$

$∴ v_{B}=\omega_{A B} \ r_{A B}$

$6.211=\omega_{ A B}(5) \Rightarrow \omega_{ A B}=1.24 \mathrm{rad} /s$

$\begin{array}{l}{16-86 . \text { As the cord unravels from the wheel's inner hub, }} \\ {\text { the wheel is rotating at } \omega=2 \text { rad/s at the instant shown. }} \\ {\text { Determine the velocities of points } A \text { and } B \text { . }}\end{array}$

$\omega=2 rad / s$

$v_A= ?, v_ B=?$

$r_{B}-I_{C}=5+2=7 i n$

$r_{A}-I_{C}=\sqrt{2^{2}+5^{2}}=\sqrt{2} 9 \text { in }$

$v_{B}=\omega r_{B}-I_{C}=2 * 7=14 \mathrm{in} / \mathrm{s}$

$v_{A}=\omega r_{A}-I_{C}=2 * \sqrt{29}=10.8 \mathrm{in} / \mathrm{s}$

$\theta=\tan ^{-1}\left(\frac{2}{5}\right)=21.8^{\circ}$