# Kinetic energy of rotation

Tags:
1. May 7, 2016

### RoboNerd

1. The problem statement, all variables and given/known data
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

2. Relevant equations
K.E. = Kinetic energy of rotation + kinetic energy of translation.

3. The attempt at a solution

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!

2. May 7, 2016

### 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.

3. May 7, 2016

### RoboNerd

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