# Rotational speed question

1. Oct 16, 2005

### willworkforfood

"The mass of the Earth is about 6x10^24 kg and its radius is about 6x10^6 meters. Suppose you build a runway along the equator, line-up a million F-16's, bolt them down, and have them all fire their engines (eastward) simultaneously for 1/2 hour. Estimate the effect that would have on the rotational speed of the Earth. Assume the thrust of each plane's engines is 30,000 lbs = 133,000 newtons."

I'm not even sure how to begin answering this question because I have no idea what it is asking for or what any equation is for "rotational speed". Is rotational speed the same thing as angular velocity? Thanks for your help

2. Oct 16, 2005

### Fermat

You have a sphere with an applied Torque (from your F-16's) giving an angular acceleration (or should that be deceleration ?)
What is the effect of this acceleration/deceleration after 1/2 hour.

rotational speed is, in effect, the angular velocity.

Last edited: Oct 16, 2005
3. Oct 16, 2005

### Chi Meson

"rotational speed" is often used if you are talking about "rotations per minute" and so forth. "Angular velocity" (represented with the lower-case omega) should specifically be in radians per second. But they are the same concept.

Look up the moment of inertia for a solid uniform sphere rotating about its center (although the earth is NOT so, I'm sure you don't need to do the calculus for the most accurate answer)

4. Oct 16, 2005

### willworkforfood

So I am basically using the equations

T=r*F*sin(angle)

and T=I*alpha

where r is radius F is force and alpha is angular acceleration to find the change in rotational speed/angular velocity, yes?

5. Oct 16, 2005

### Chi Meson

Yes, so far so good. The angle will be 90 degrees. After finding angular acceleration, find the change in angular velocity which is (alpha)t. Remember to change earth's ang velocity to radians per second.