Angular acceleration, density question

[letsfailsafe]

Homework Statement

First question:
"A DVD player can exert a torque on a DVD of 10−3 N⋅m. What is the DVD’s angular acceleration in rad/s2?

Details and assumptions

• The DVD has a mass of 0.015 kg and a radius of 0.06 m.
• A DVD can be modeled as a thin uniform cylinder.

"

Second question:
"A cube of ice 2 cm on a side is floating in a glass of water. You observe that the top of the ice is 0.166 cm above the surface of the water. What is the ratio of the density of ice to the density of water?"

Homework Equations

First question:
α = $\tau$ / I
I = Ʃmr²

The Attempt at a Solution

First question:
α = 0.001 / ((0.015)(0.06)²)
= 18.5185

Not sure how I can do the second question at all...
I've got these two questions from the internet.
Please help me solve these question.

 

[haruspex]

α = 0.001 / ((0.015)(0.06)²)
= 18.5185

Yes, given the problem statement, but I'm astonished a DVD is to be modeled as a thin cylinder. A disc would be more reasonable, and that would change the answer.

For the 2nd problem (in future, pls use separate threads for unrelated problems), what determines the volume of the ice that will be below water?

 

[letsfailsafe]

α = 0.001 / ((0.015)(0.06)2)
= 18.5185

is not right...

 

[Basic_Physics]

1. The moment of inertia of a disc or thin cylinder is

I = 1/2 Mr²

so you are out by a factor of 2.

2. For this question you can start out with Archimedes' principle which states that the buoyant force on an object is equal to the weight of the liquid that it displaces.

 

[haruspex]

1. The moment of inertia of a disc or thin cylinder is
I = 1/2 Mr²

For a disc, yes, but not for a thin cylinder about its axis. And it does say cylinder, strange though that is.
Perhaps it meant short fat cylinder, but then why not just say disc?

 

[Basic_Physics]

A thin solid cylinder would be a disc?

 

[lep11]

Maybe I usually help 'too much'... To get started, think about the forces acting on the ice cube.
ƩF=0 ⇔
G=N...

 

[haruspex]

A thin solid cylinder would be a disc?

It doesn't say solid, you've added that. The most obvious interpretation of 'thin cylinder' is that it is a tube with a thin wall, i.e. the cross-section has a narrow annulus. If it means thin the other way, why not say a very short solid cylinder, or even more naturally, a disc? But it is quite possible that the question is just very poorly worded.