Angular velocity and moment of inertia

[kikidoll]

Could you let me know if my answers are correct?

Homework Statement

A light rope is wrapped several times around a large wheel with a radius of 0.400m. The wheel rotates in frictionless bearings about a stationary horizontal axis. The free end of the rope is tied to a suitcase with a mass of 0.15kg. The suitcase is released from rest at a height of 4.00m above the ground. The suitcase has a speed of 3.50 m/s when it reaches the ground.
Calculate:
A) the angular velocity of the wheel when it reaches the ground and
B) the moment of inertia of the wheel

Homework Equations

A) angular velocity (w) = speed/radius
B) mgh = 1/2 mv² + 1/2Iw²

The Attempt at a Solution

After using these equations I found angular velocity to be 8.75 rad/s and the moment of inertia to be 12.9 kg*m².

Correct or incorrect? Thanks for you help.

 

[LowlyPion]

Could you let me know if my answers are correct?

Homework Statement

A light rope is wrapped several times around a large wheel with a radius of 0.400m. The wheel rotates in frictionless bearings about a stationary horizontal axis. The free end of the rope is tied to a suitcase with a mass of 0.15kg. The suitcase is released from rest at a height of 4.00m above the ground. The suitcase has a speed of 3.50 m/s when it reaches the ground.
Calculate:
A) the angular velocity of the wheel when it reaches the ground and
B) the moment of inertia of the wheel

Homework Equations

A) angular velocity (w) = speed/radius
B) mgh = 1/2 mv² + 1/2Iw²

The Attempt at a Solution

After using these equations I found angular velocity to be 8.75 rad/s and the moment of inertia to be 12.9 kg*m².

Correct or incorrect? Thanks for you help.

With ω = v/r then 8.75 looks ok.

But your I looks a little large.

m*g*h is total energy to start with dividing by ω² where ω² looks a lot bigger than m*g*h doesn't look right.

 

[kikidoll]

Thanks for the reply. I also though I was rather large, but with my calculations that's what I ended up getting... strange.

 

[LowlyPion]

Thanks for the reply. I also though I was rather large, but with my calculations that's what I ended up getting... strange.

I think you've done something wrong.

Maybe show your numbers and how you got there.

 

[kikidoll]

A) w = v/r = (3.50)/(0.400) = 8.75 rad/s

B) Ki + Ui = Kf + Uf
Ki and Uf = 0

Ui = Kf
mgh = 1/2 mv² + 1/2Iw²
(15)(9.8)(4) = 1/2 (15)(3.5)² + 1/2 (I) (8.75)²
588 = 91.9 + 38.3(I)
496.1 = 38.3(I)
I = 12.9 kgm²

 

[LowlyPion]

A) w = v/r = (3.50)/(0.400) = 8.75 rad/s

B) Ki + Ui = Kf + Uf
Ki and Uf = 0

Ui = Kf
mgh = 1/2 mv² + 1/2Iw²
(15)(9.8)(4) = 1/2 (15)(3.5)² + 1/2 (I) (8.75)²
588 = 91.9 + 38.3(I)
496.1 = 38.3(I)
I = 12.9 kgm²

Whoa. SI units please.

m = .15kg

 

[kikidoll]

Oh my gosh I can't believe I did that *facepalms*

Thanks for your help, I really appreciate it