Answer:
a) W = 2rad/s
b)
Explanation:
part a. (the angular velocity of the bar just after it hit by the bird)
using the conservationof the angular momentum:
so:
where M is the mass of the bird, V the velocity of the bird, d the lever arm, I the moment of inerta of the bar and W the angular velocity of the bar just after the collition.
Now we have to find the moment of inertia of the bar as:
I =
Where M is the mass of the bar and L the length of the bar. So, I is equal to:
I =
I = 0.5 kg*m^2
Then, replacing values on the first equation, we get:
Solving for W:
W = 2rad/s
part b. (the angular velocity of the bar just as it reaches the ground)
we will use the conservation of energy:
so:
Where is the mass of the bar, g is the gravity, h the altitude of the center of mass and the angular velocity of the bar just as it reaches the ground.
Then, replacing values, we get:
Finally, solving for :