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Q 12CQ

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Found in: Page 353

### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# Question: The Earth has more rotational kinetic energy now than did the cloud of gas and dust from which it formed. Where did this energy come from?

The rotational kinetic energy increased due collapsing of the clouds under its own gravitational force.

See the step by step solution

## Step 1: Concept of rotational kinetic energy.

Rotational kinetic energy is caused due to rotation of an object. It is proportional to the rotational inertia and the square of the magnitude of the angular velocity.

Mathematically,

$$K.E{._{rot.}} = \frac{1}{2}I{\omega ^2}$$

Here;

I is the moment of inertia and

$$\omega$$is the angular velocity

## Step 2: Explanation for greater rotational kinetic energy of Earth at present than earlier.

Earlier, the solar system was composed of massive cloud of gas and dust and it was slowly rotating. The cloud started to spin faster when they collapsed under its own gravitational pull, resulting in faster spinning of the clouds. This faster spinning is similar to an ice skater pulling his arms to spin faster. The planet rotated along with all the material that accreted to form the planet. This led to the increase in rotational kinetic energy at present.