Question

If bar \(A B\) has angular velocity and acceleration, \(\vec{\omega}_{A B}=-4 \vec{k} \mathrm{rad} / \mathrm{s}\) and \(\vec{\alpha}_{A B}=\) \(-1 \vec{k} \mathrm{rad} / \mathrm{s}^{2}\), respectively. The angular velocity and acceleration of the member \(B C\) are also found to be \(\vec{\omega}_{B C}=-3 \vec{k} \mathrm{rad} / \mathrm{s}\) and \(\vec{\alpha}_{B C}=-37.122 \vec{k} \mathrm{rad} / \mathrm{s}^{2}\). Answer the following questions:

\(\mathrm{A}[20 \%] \tilde{r}_{C / B}=\) \(\tilde{i}+\) \(\tilde{j}\)

B [20\%] Draw the vector \(\vec{\alpha}_{B C} \times \vec{r}_{C / B}\) in the bar figure below.

C \([20 \%]\) Draw the vector \(\vec{\omega}_{B C} \times\left(\vec{\omega}_{B C} \times \vec{r}_{C / B}\right)\) in the bar figure below.

D [40\%] Use relative motion analysis to find \(\vec{a}_{C}\).

Answer 1