The angular speed of the turntable with a woman on it? Help

[riseofphoenix]

The angular speed of the turntable with a woman on it? Help!

Ok so I understand part a (why it's counterclockwise. τ = Fr = (mg)(2) = (70)(9.8)(2) = +1372)

Part b is where I'm stuck...
This is what I did...

PE_initial + [STRIKE]KE_{initial rotational}[/STRIKE] = [STRIKE]PE_final[/STRIKE] + KE_{final rotational}
PE_initial = KE_{final rotational}
mgh = (1/2)Iω²
(70)(9.8)(2) = (1/2)(540)ω²
1372 = 270ω²
1372/270 = ω²
5.08 = ω²
2.25 rev/s = ω

Convert to rad/s

2.25/2π rad/s = 0.358 rad/s, but the answer is 0.389.
Help! :( Where did I go wrong?

 

[grzz]

Did the woman change her position in the VERTICAL direction?

 

[riseofphoenix]

Brb in 2 hours!
In the meantime can someone answer my question?

 

[riseofphoenix]

Did the woman change her position in the VERTICAL direction?

No/yes?

Hold on! I have to go to class real quick!
brb!

 

[voko]

Is angular momentum conserved here?

 

[grzz]

If the OP is to learn anything then the OP must try to answer the question posted above, i.e. whether the woman changed her position in the vertical direction.

 

[riseofphoenix]

Is angular momentum conserved here?

Yes! She maintains a constant speed of 1.50 m/s, so the round table keeps turning (conservation of angular momentum)

L = Iω

 

[riseofphoenix]

If the OP is to learn anything then the OP must try to answer the question posted above, i.e. whether the woman changed her position in the vertical direction.

Wait what?

 

[aralbrec]

The woman is walking on a surface that stays horizontal. You've misunderstood the question.

 

[riseofphoenix]

The woman is walking on a surface that stays horizontal. You've misunderstood the question.

Wait are you talking to me?

 

[voko]

Yes! She maintains a constant speed of 1.50 m/s, so the round table keeps turning (conservation of angular momentum)

L = Iω

The total angular momentum of the entire system is conserved regardless of constancy of her speed. This is because there are no external forces acting on the system. How could you use this fact?

 

[riseofphoenix]

The total angular momentum of the entire system is conserved regardless of constancy of her speed. This is because there are no external forces acting on the system. How could you use this fact?

1) Conservation of angular momentum (NO EXTERNAL FORCES acting on the system)

L_initial = L_final
[STRIKE](L_table + L_woman)_initial[/STRIKE] = (L_table + L_woman)_final
0 = (L_table + L_woman)_final
0 = I₁ω₁ + I₂ω₂
-I₁ω₁ = I₂ω₂
ω₁ = -(I₂ω₂)/I₁

2) Moment of Inertia for the woman (I₂)

I₂ = mr²
I₂ = (70)(2²)
I₂ = 280

3) Angular Speed of the woman (ω₂)

ω = v/r
ω = (1.50)/(2)
ω = 0.75 rad/s

4) Moment of Inertia for the table (I₁) - this is given

I₁ = 540

5) Plug and chug

ω₁ = -(I₂ω₂)/I₁
ω₁ = -[(-280)(0.75)]/540
ω₁ = 0.389 rad/s

 

[riseofphoenix]

Merci!