Calculating Moment of Inertia for Rotating Objects: A Kinetic Energy Problem

[RoboNerd]

Homework Statement

1. What is the moment of inertia of a spinning object of radius 0.5 m and mass 6 kg moving at 5 m/s, if it has a kinetic energy of 100 J?
   
   1. 1) 1 kgm2
   2. 2) 2 kgm2
   3. 3) 4 kgm2
   4. 4) 8 kgm2
   5. 5) 20 kgm2
      

Homework Equations

K.E. = Kinetic energy of rotation + kinetic energy of translation.

The Attempt at a Solution

[/B]
Hi everyone. I keep trying to solve this and I get the answer to be 0.5 kgm^2.

Obviously, this is not an answer. They say that the answer is 2).

Here's what I did:

(1 / 2) * m * v^2 + (1 /2) * I * omega^2 = 100.

(1 / 2) * 6 * 5^2 + (1 /2) * I * (v^2 / r^2)^2 = 100.

Rearrange to get I = (r^2 / v^2 ) * 50 = 0.5

Why do I not stack up with what the authors have written here? Thanks in advance for the help!

 

[TSny]

The statement of the problem is fuzzy. You can get answer (2) if you assume that the object is rotating about a fixed axis and assume that the 5 m/s represents the linear speed of a point located a distance 0.5 m from the axis of rotation.

 

[RoboNerd]

OK, so I do not need to worry about it. Thanks a lot.