If earth were to shrink suddenly, what would happen to the length of the day ?

Explanation

To solve the problem of how the length of the day would change if the Earth were to suddenly shrink, we can follow these steps:

### Step 1: Understand the Concept of Angular Momentum
The length of the day is determined by the rotation of the Earth around its axis, which is characterized by its angular momentum. Angular momentum (L) is given by the product of the moment of inertia (I) and the angular velocity (ω):
\[ L = I \cdot \omega \]

### Step 2: Define the Moment of Inertia
For a solid sphere like Earth, the moment of inertia is given by:
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