Angular momentum and change in velocity

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A turntable with a moment of inertia of 2.5 x 10^-2 kg m² spins at 33.3 rev/min when a 0.25 kg ball of putty is dropped on it, affecting its angular speed. The initial attempt to calculate the new angular speed using the equation Iω = (I + mr)ω(final) resulted in an incorrect answer of 27 rev/min, while the correct answer is 24 rev/min. The error was identified as a misunderstanding of the units involved, specifically that mr does not have the same units as moment of inertia (I). Proper application of angular momentum conservation principles is crucial for accurate calculations in such scenarios. Understanding the relationship between moment of inertia and angular velocity is essential for solving similar physics problems.
physgrl
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Homework Statement



A turntable has a moment of inertia of 2.5 x 10-2 kg m2 and spins freely at 33.3 rev/min. A 0.25 kg ball of putty is dropped vertically on the turntable at a point 0.20 m from the center. What is the new angular speed of the system?

a. 41 rev/min
b. 24 rev/min
c. 33 rev/min
d. 27 rev/min


Homework Equations



L=Iω
p=mv
L=r*p

The Attempt at a Solution



i tried to do Iω=(I+mr)ω(final)
i got 27 rev/min
the real answer is supposed to be 24rev/min according to the answer key
 
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physgrl said:

Homework Statement



A turntable has a moment of inertia of 2.5 x 10-2 kg m2 and spins freely at 33.3 rev/min. A 0.25 kg ball of putty is dropped vertically on the turntable at a point 0.20 m from the center. What is the new angular speed of the system?

a. 41 rev/min
b. 24 rev/min
c. 33 rev/min
d. 27 rev/min


Homework Equations



L=Iω
p=mv
L=r*p

The Attempt at a Solution



i tried to do Iω=(I+mr)ω(final)
i got 27 rev/min
the real answer is supposed to be 24rev/min according to the answer key

Can you show the details of your calculation? We can't tell you what you did wrong if you don't show us your work!
 
"i tried to do Iω=(I+mr)ω(final)"

Careful, mr does not have same units as I.
 
Yeah that was my error thanks!
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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