Collision between ball and stick

[juggalomike]

Homework Statement

On a frictionless table, a 0.58 kg glob of clay strikes a uniform 1.62 kg bar perpendicularly at a point 0.18 m from the center of the bar and sticks to it. If the bar is 0.70 m long and the clay is moving at 6.20 m/s before striking the bar, what is the final speed of the center of mass?
A=1.63m/s

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

[PLAIN]http://img217.imageshack.us/img217/616/prob21a.gif

Homework Equations

Not sure

The Attempt at a Solution

I solved for the final speed of the center of mass using conservation of momentum, but i am lost on the 2nd part. I know the center of mass changes when the clay is attached to the bar, but I am not sure how i would use that to solve the question.

 

[tiny-tim]

Hi juggalomike!

Use conservation of angular momentum …

what do you get? ​

 

[juggalomike]

Hi juggalomike!

Use conservation of angular momentum …

what do you get? ​

If i using conservation of angular momentum, which is Ii*Wi=If*Wf the initial side will be 0 because initialy it has no angular velocity?

 

[collinsmark]

Hello juggalomike,

Think about what is the center of mass of the system (the system being the combination of bar and glob) immediately before impact. Using that point as the center of mass, what is angular momentum (before impact) associated with the bar? And the glob?

 

[rdl]

I would approach this problem by first analyzing the collision between the ball and stick using the principles of conservation of momentum and conservation of energy. Since the collision is perfectly inelastic (the two objects stick together after the collision), we can use the equation:

m1v1 + m2v2 = (m1 + m2)v

where m1 and v1 are the mass and initial velocity of the clay, m2 and v2 are the mass and initial velocity of the stick, and v is the final velocity of the combined system. Plugging in the given values, we can solve for v which gives us the final speed of the center of mass.

To determine the angular speed of the system after the impact, we can use the equation:

L = Iω

where L is the angular momentum, I is the moment of inertia, and ω is the angular speed. Since the collision is perpendicular to the stick, the moment of inertia can be calculated using the equation:

I = Σmiri^2

where Σm is the sum of the masses of the clay and the stick, and ri is the distance of each mass from the center of mass. We can then use the equation for conservation of angular momentum:

L1 = L2

where L1 is the initial angular momentum (which is zero since the stick is initially at rest) and L2 is the final angular momentum. Plugging in the calculated moment of inertia and the final velocity of the center of mass, we can solve for ω which gives us the angular speed of the system after the impact.