(a) 2.42 J
The kinetic energy of a rotating object is given by:
where
I is the moment of inertia
is the angular speed
Here we have
at the lowest point of the trajectory
While the moment of inertia of a rod rotating around one end is
And substituting in the previous formula, we find the kinetic energy at the lowest position:
(b) 0.99 m
According to the law of conservation of energy, the total mechanical energy (sum of kinetic energy and potential energy) must be conserved:
At the lowest point, we can take the potential energy as zero, so the mechanical energy is just kinetic energy:
At the highest point in the trajectory, the rod is stationary, so the kinetic energy will be zero, and the mechanical energy will simply be equal to the gravitational potential energy:
where h is the heigth of the centre of mass of the rod with respect to the lowest point of the trajectory. Solving for h, we find