# Kinetic energy of rotation

• 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

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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!

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.