- #1

- 488

- 4

For example, assume a long thin bar with mass M and length L hanging from a fixed frictionless point A at the ceiling, the bar is stay at rest. Now a bullet with mass m and initial velocity [tex]v_0[/tex] moving horizontally towards the bar and hit it at point B (the distance b/w A and B is y). Finally, the bullet embed into bar and then moving together with it. The instantaneous horizontal impulse when it hit the bar is [tex]I_b[/tex], find the intial angular velocity of the bar.

Since the system's total momentum is conserved, we can write

[tex]

mv_0 = (m+M)V_f

[/tex]

and the change of the momentum of the bullet is the impulse

[tex]

MV_f = -m(v_f-v_0) = -I_b

[/tex]

then the initial angular momentum of bar can be given by

[tex]

L = MV_f y = -I_b y

[/tex]

After collision, the bar (and the bullet) move around pivot A, the moment of inertia about A is [tex]I=ML^2/3[/tex] (ignore the mass of bullet). With the help of following equation

[tex]L = I\omega[/tex]

we find that

[tex]\omega = \frac{L}{I} = - \frac{3I_b y}{ML^2}[/tex]

the result (the value) is correct, but it should be positive. I have no idea where is the mistake come from.