Question

The problem describes a rigid rod connecting two masses, 'm' and '2m', with a length 'l'. The mass '2m' is given an instantaneous horizontal velocity 'v'. We need to find the angular velocity of the system immediately after this impulse.

Answer 1

The angular velocity of the system is $\frac{v}{l}$.

Answer 2

The system's motion is a combination of translation and rotation. We first find the velocity of the center of mass using the impulse-momentum theorem. Then, using the rigid body velocity formula ($V_P = V_{CM} + \vec{\omega} \times \vec{r}_{P/CM}$) applied to the mass '2m', whose velocity is known, we solve for the angular velocity $\omega$. Alternatively, recognizing that the mass 'm' comes to instantaneous rest, it acts as the instantaneous center of rotation, simplifying the calculation of $\omega$.