Can Rotational Kinematics be Used to Solve this Problem?

[tanzl]

The question and solution is here
http://i359.photobucket.com/albums/oo31/tanzl/Set4Problem3.jpg

The solution is quite long. Is there any way I can use conservation of momentum (translational or rotation) to calculate this question? such as
initial momentum of ball = final momentum of ball + final momentum of plank
Since the plank does not have any translational motion at its center of mass, then its momentum is zero.
But, I think it won't works because pivot actually exerts force on the plank to constraint its translational motion. So, the system is not closed.

 

[jbsteele]

Yes, you can use conservation of momentum to calculate this question. For the translational motion of the ball, it is the same as the equation you provided: initial momentum of ball = final momentum of ball + final momentum of plankFor the rotational motion of the plank, you can use conservation of angular momentum. The equation for this is:initial angular momentum = final angular momentumYou can then determine the initial and final angular momenta of the plank and solve for the unknowns.

 

[baba89]

Yes, you are correct in your thinking that conservation of momentum cannot be used in this situation. This is because the plank is not a closed system - it is being acted upon by an external force (the pivot) which is not accounted for in the conservation of momentum equation. In rotational kinematics, we must consider the rotational motion of the plank and use equations such as torque and angular acceleration to solve for the final angular velocity of the plank. This is a more appropriate approach for this type of problem.