Solving the Problem of Angular Speed After Clay Striking Bar

[zhenyazh]

Hi
i am preparing for the test and i have a problem with the following question.
an image is attached.

On a frictionless table, a glob of clay of mass 0.30 kg strikes a bar of mass 1.20 kg perpendicularly at a point 0.22 m from the center of the bar and sticks to it.

If the bar is 1.34 m long and the clay is moving at 7.3 m/s before striking the bar, what is the final speed of the center of mass?
this i have found 1.460 m/s

At what angular speed does the bar/clay system rotate about its center of mass after the impact?

i am quite confused here.
can u show me how to solve this.
especially as i know i need to find the distance between my the center of mass and the point with respect to which i calculate - how do i calculate the center of mass.
it is a weighed average between distances from the respect point, but what is the distance of the bar. do i use its length or the distance from one side to the place where the clay is?

 

[zhenyazh]

anyone? :)

 

[kuruman]

This is an inelastic collision that does not conserve mechanical energy. You need to conserve angular momentum about the center of mass of the rod and linear momentum. Your unknowns are the speed of the center of mass after the collision and the angular speed ω.

 

[zhenyazh]

sure, so far i knew i should do it too.
but take a look at the last paragraph of what I've written. i think i am doing the calculation o mention there wrong and this is why i get a wrong result.

 

[kuruman]

If I understand correctly you want to know how to find the center of mass of the composite system. Don't forget that the rod can be viewed as having its entire mass at its midpoint. This is what you do

1. Define your origin (with respect to which you measure all distances) to be the midpoint of the rod.
2. Let M be the mass of the rod, m be the mass of the glob and d the position of the glob after it is stuck on the rod.

Then the position of the center of mass of the composite is given by

$$X=\frac{M \times 0 + m \times d}{M+m}$$

Is this what you were looking for?

 

[zhenyazh]

hi
i am still confused.
no matter what i do i can't get the correct result.
could please write the solution outline in parameters? or at least describe
each stage of the solution?

thanks