Conservation of angular momentum

[Mohammeddev]

Homework Statement

A rod of length D sits at rest on a friction less table. A ball of mass M strikes the end of the rod with a speed V and rebounds with a speed 3v/4 causing the rod to rotate counterclockwise around a fixed axis at one end. The rotational inertia of the rod is I

Homework Equations

Li = Lf

The Attempt at a Solution

the question is :
What is the angular velocity ω of the rod after the collision?
We know that the initial angular momentum is equal to the final angular momentum so i started with the ball because it's the only object in our system that has initial angular momentum:

MvD = -3MvD/4 + IW

doing some algebra:
MvD * 4 = -3MvD + IW
4MvD + 3MvD = IW
7MvD = IW
W = 7MvD/I

But the correct answer is :
7MvD/4I
my question where did the 4 come from ?
is my math Wrong ?

 

[DrClaude]

MvD = -3MvD/4 + IW

doing some algebra:
MvD * 4 = -3MvD + IW

Check what you are doing to go from the first equality to the second.
.

 

[Mohammeddev]

Check what you are doing to go from the first equality to the second.
.

Okay now i realized the mistake i made Thank you for making me recheck my answer i was so convinced that khan academy is wrong in this one !