Rotation of Rod Homework: Max Angle, Motion Analysis

[rbwang1225]

Homework Statement

A uniform thin rod with mass M and length L nailed by frictionless pivot can swing freely on the wall as shown in Fig. The pivot locates at the distance L/4 from the bottom and stops inside. The velocity of the bullet before hitting the rod is v. (a) Compute the max. angle that the rod can reach after the shot. (b) If the swinging angle is small, describe the motion of the whole system (rod+bullet) in detail.

The Attempt at a Solution

I used the conservation of energy and concept of mass center.
The result of (a) is $cos\theta = \frac{2mv^2-(M+2m)gL}{L(1+\frac{m}M)}$.
I don't really understand how to get (b).

 

[tiny-tim]

hi rbwang1225!

I used the conservation of energy …

nooo …

energy is never conserved in a collision unless the question says so

in this case, energy is obviously not conserved, since the bullet becomes part of the rod, and the collision is perfectly inelastic

however, momentum or angular momentum is always conserved in a collision ​

(for b, the system becomes a pendulum, with shm)

 

[rbwang1225]

hi rbwang1225!


nooo …

energy is never conserved in a collision unless the question says so

in this case, energy is obviously not conserved, since the bullet becomes part of the rod, and the collision is perfectly inelastic

however, momentum or angular momentum is always conserved in a collision ​

(for b, the system becomes a pendulum, with shm)

Oh...right! I forgot the reason why the bullet stuck in the rod!
Now that means I have to calculate the moments of the inertia...
I know it would be a SHM but how do I describe "in detail"?
Thanks a lot!

 

[tiny-tim]

I know it would be a SHM but how do I describe "in detail"?

τ = Iα