# If the polar ice caps melted, would a day be longer or shorter?

1. Nov 11, 2005

### confusedbyphysics

If they melted and water was evenly distributed all over the earth.

From what I guess I should use angular momentum. Ang momentum = I (moment of intertia) X W (angular velocity)

I = mr^2 for a thin hoop...I think I use this for the ice caps

and I for a uniform sphere is 2/5mr^2

so since the uniform sphere will make the angular momentum less, the earth will turn slower and the day will be longer?

does this sound right? or do the two angular momentums need to be set equal to eachother? am i on the right track? thanks

2. Nov 11, 2005

### Staff: Mentor

The angular momentum doesn't change; since there's no external torque on the earth, the angular momentum is conserved. What matters is how the rotational inertia of the "earth + ice/water" changes as the ice melts. Does the rotational inertia increase or decrease?

3. Nov 11, 2005

### confusedbyphysics

The rotation inertia increases because the mass is distributed in more parts around the earth? that means the earth moves faster though, doesnt it? im confused

4. Nov 11, 2005

### Staff: Mentor

The rotational inertia increases because the mass is redistributed further away from the axis of rotation.

How does angular momentum relate to angular speed and rotational inertia?

5. Nov 11, 2005

### confusedbyphysics

Ang mom. = intertia X ang. speed.

I = all the mr^2 added together

6. Nov 11, 2005

### Staff: Mentor

Good. So, if you understand that redistributions of mass on the earth cannot affect the rotational inertia, what can you conclude about the angular speed if the ice caps melt?

7. Nov 11, 2005

### confusedbyphysics

if ang. momentum is conserved, and intertia goes up, speed must go down...so the days are longer?

8. Nov 11, 2005

### Staff: Mentor

You got it.

9. Nov 11, 2005

### confusedbyphysics

cool, thanks for the help Doc Al, much appreciated!