Determine the sign of angular momentum

[MechaMZ]

Homework Statement

A 2 kg disk traveling at 3 m/s strikes a 1 kg stick of length 4 m that is lying flat on nearly frictionless ice .Assume the collision is elastic and the disk does not deviate from its original line of motion. Find the translational speed of the disk, the translational speed of the stick, and the angular speed of the stick after collision. The moment of inertia of the stick about center of mass is 1.33 kg m²

Attempt:

conservation. of linear momentum

m_dv_di = m_dv_df + m_sv_s
(2 kg) (3 m/s)=(2 kg) v_df + (1 kg)v_s
6 kg m/s-(2 kg) v_df = (1 kg)v_s----------------------(1)

conservation. of angular momentum
-rm_dv_di = -rm_dv_df + I*omega
-12kgm²/s=(- 4kg m) v_df + (1.33 kg m²)*omega----------------------(2)
-9rad/s+(3rad/m) v_df = omega

elastic collision
1/2 m_dv_di² = 1/2m_dv_df² +1/2 I*omega² + 1/2m_sv_s²
18 m² /s² =2m_dv_df² +(1.33 m2 )*omega² + v_s²--------------------------(3)

solve .(1), (2), (3) >>> vdf =2.3 m/s, omega = -2rad/s , vs =1.3 m/s



For my solution above, I have no idea why the rm_dv_di and rm_dv_df are negative, but I*omega is positive. I tried to figure it with right hand rule, but i still find three of them should be in the same direction.

 

[MechaMZ]

Hi, could anyone help me to figure out the reason?
I still don't get it =(

 

[MechaMZ]

anyone knows? perhaps i attach a picture to explain the motion better.

http://img97.imageshack.us/img97/4315/rotation.jpg