Conservation of Angular Momentum Problem Help

[yus310]

Homework Statement

Ok... "A small bob of putty of mass m falls from the ceiling and lands on the outer rim of a turntable of radius R and moment of inertia I_0 that is rotating freely with angular speed of w_i, about its vertical fixed symmetry axis..."

"After several turns the blob flies off the edge of the turntable. What is the angular speed of the turntable after the blob flies off."

Homework Equations

The Attempt at a Solution

Ok.. so angular momentum is conserved... so when the blob hits the turn table

..
I_0*w_i=(I_0+m*R^2)w_f

Solve for w_f...

but when the blob flies off, do they does the final angular velocities of the turntable and putty different or similar? Does the putty fly off with a velocity of w_f or something else... does this look logical?

Angular Momentum Initial= Angular Momentum Final...
But what next?

 

[yus310]

Additional Question

Additional Question...
Go to...

http://www.nd.edu/~agoussio/10310_spring2006/2006_exam3.pdf

MC5

... Wouldn't the answer be that w_0=w_f... because when you put two things in the opposite direction, that means they'll be moving at the same velocity... is this right? Or it is that they'll move slower and w_0>w_f...

.5*m*w_0*(3R^2)=.5*m*w_f*(R^2)?

Wrong or Right? Thanks.

 

[m2003]

Your approach to solving the problem seems logical. The conservation of angular momentum equation you have written is correct. To solve for w_f, you can rearrange the equation to get:

w_f = (I_0*w_i)/(I_0+m*R^2)

After the blob flies off, the final angular velocity of the turntable will be different from the initial angular velocity, since the mass of the blob has now been added to the turntable. The blob itself will also have a different angular velocity, which can be calculated using the same equation. So, the final velocities of the turntable and the blob will be different.

To solve for the final angular velocity of the blob, you can use the same equation, but with a different moment of inertia (since the blob will have a different shape and mass compared to the turntable). You can use the moment of inertia of a solid cylinder or disk for the blob's moment of inertia.

Overall, your approach to solving the problem is correct. Just make sure to use the correct moment of inertia for the blob and solve for both the final angular velocities of the turntable and the blob.