Mechanical System: Kinetic Energy of a Rotating Bar with Gravity

[Goklayeh]

Consider a mechanical system (subject to gravity) consisting of an homogeneous bar, lying in the $$xy$$ -plane, of mass $$m$$, length $$\ell$$ and negligible section, with an extreme hinged in a fixed point $$P$$ of the $$y$$ axis. Now, suppose that the $$y$$-axis is rotating with angular velocity $$\omega = \omega(t)$$. What is the kinetic energy of the system?

 

[tiny-tim]

Hi Goklayeh!

(have an omega: ω )

KE of rigid body = rotational energy (about c.o.m.) plus energy of total mass with same velocity as c.o.m.

(or use the parallel axis theorem)