How Can Velocity and Angular Momentum Be Calculated in These Dynamics Problems?

[rock.freak667]

Homework Statement

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Homework Equations

The Attempt at a Solution

For the first one, the solutions are different from mine, but here is what I did:

Note $\times$ denotes the cross-product

$$v_B=\vec{\omega_B} \times \vec{r_{CB}}$$
$$v_B=2.5k \times 0.045j=-0.1125j$$

$$v_A=\vec{\omega_A} \times \vec{r_{OA}}$$
[tex]v_A= 3k \times 0.06i=0.18j<br /> <br /> $$\vec{v_{AB}}=\vec{v_A}-\vec{v_B}=0.1125i+0.18j$$<br /> <br /> Now, $\vec{r_{AB}}= 0.09i+0.12j$<br /> <br /> $$\vec{\omega_{AB}} \times \vec{r_{AB}}= w_{AB}k \times (0.09i+0.12j)$$<br /> $$\Rightarrow \vec{v_{AB}}=-0.12 \omega_{AB}i+0.09\omega_{AB}j$$<br /> <br /> <br /> and if I compare components I get two different values for $\omega$<br /> <br /> <br /> For the second question, the first thing I'd do is get the moment of inertia of the rod about the centre using (1/12)mL^2 and then say Ia=Torque to get a, then use F=ar to get the force needed. But I do not know if I should assume the rod is uniform and use the parallel axis theorem.<br /> <br /> For the third one, I am not too sure how to start that one. All I know that I can get from reading the question is the moment of inertia about the axis using the radius of gyration.[/tex]