# A few dynamics questions

1. Mar 29, 2009

### rock.freak667

1. The problem statement, all variables and given/known data

http://img18.imageshack.us/img18/4180/82081641.jpg [Broken]
http://img14.imageshack.us/img14/2650/26169677.jpg [Broken]

http://img13.imageshack.us/img13/6657/diagramsx.jpg [Broken]

2. Relevant equations

3. 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

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

$$v_A=\vec{\omega_A} \times \vec{r_{OA}}$$
$$v_A= 3k \times 0.06i=0.18j [tex]\vec{v_{AB}}=\vec{v_A}-\vec{v_B}=0.1125i+0.18j$$

Now, $\vec{r_{AB}}= 0.09i+0.12j$

$$\vec{\omega_{AB}} \times \vec{r_{AB}}= w_{AB}k \times (0.09i+0.12j)$$
$$\Rightarrow \vec{v_{AB}}=-0.12 \omega_{AB}i+0.09\omega_{AB}j$$

and if I compare components I get two different values for $\omega$

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.

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.

Last edited by a moderator: May 4, 2017