Global Warming. If the earth’s climate continues to warm, ice near the poles will melt, and the water will be added to the oceans. What effect will this have on the length of the day? Justify your answer. (Hint: Consult a map to see where the oceans lie.)

The moment of inertia for a point mass is just the mass times the square of the distance perpendicular to the rotation axis. Which is given by

$\mathit{l}\mathbf{=}\mathit{M}{\mathit{R}}^{\mathbf{2}}$

lis the moment of inertia and is mass of the object and is the radius of the object.

Here we have the situation that the earth’s climate continues to warm, ice near the poles will melt, and the water will be added to the oceans.

The earth's equator line's radius$\left(R_e\right)$ is greater than the radius to the poles $\left(R_p\right)$. At the poles, the ice mass is located nearer to the axis of rotation. There will be more mass surrounding the equator line because after melting, the water flows to the equator. More mass is located farther from the axis of rotation as a result of the process.

Since$R_e>R_p\Rightarrow {R_e}^2>{R_p}^2$

Now, from equation (1),

$M{R_e}^2>M{R_p}^2$

So, When the ice melts and is dispersed along the equator, the moment of inertia is larger. Since momentum must be conserved, if the earth's moment of inertia increases and its angular speed drops, the earth will take longer to complete its rotation around its axis of rotation, lengthening the day

Hence, the day will be longer.