It doesn't change direction. It still moves straight.
Are you thinking of the Earth as just revolving around the sun and rotating? It revolves around the sun at only about 13% the speed revolves around the galaxy.
Maybe you can help me help you. If 1kg object has 212000 kg m/s of momentum at a 112 degree angle, how much force does it take to move it 6,378.10km over 6 hours at a 336.56 degree angle?
Are you assuming motion on a 2D plane with no gravity?
For now, yes. if you want to calculate it in 3D, go ahead.
OK. I will assume deceleration, stop, then acceleration; it's the only way the "move it X km over Y hours" makes sense.
The object decelerates for 60 seconds at 3533.33 m/s^2. This requires a force of 3533.33 netwons (1kg mass.) At the end of 60 seconds the mass is at rest; its momentum is zero. It then accelerates at the same acceleration for 60 seconds at a different angle. For the purposes of this problem the acceleration (and force) can be considered constant. At the end of the next 60 seconds it has reached a speed of 212,000 m/s and has covered 6,378,100 meters.
Ok, if the Earth does this when it rotates, how does it not cause a normal force? It slows is down and speeds us up relative to the center of the Earth all the time. It does it differently than the way you described, but I don't understand how it doesn't cause some force on our bodies.
Ok, if the Earth does this when it rotates, how does it not cause a normal force?
It slows is down and speeds us up relative to the center of the Earth all the time.
It does it differently than the way you described, but I don't understand how it doesn't cause some force on our bodies.
I think the point is that the Earth doesn't do this just by rotating. You need 3500 N of force pulling the object toward the center of the Earth to keep it on the surface, but the normal force can only push the object away from the center of the Earth. And the Earth's rotation hardly effects the normal force at all. Gravity is the only thing that could provide the 3500 N.
If the Earth suddenly stopped rotating, but continued to move the same way it does otherwise, would an object on it's surface really fly of in a direction tangent to the rotation of the Earth, or would it just stop with the surface?
If the Earth suddenly stopped rotating you would find yourself suddenly moving at ~1000mph East. If your path were not interrupted by any trees/walls/rocks etc you would tumble and slide until you came to a stop. You would be very slightly heavier, but if you were still alive you would not immediately notice any other differences (other than, of course, lots of things flying across the ground at 1000 mph.)
Eventually one side of the planet would freeze and one side would bake, of course.
(Ask yourself what would happen if you were on a train going 1000 mph eastwards and stepped out the back of it onto the track. Same basic answer.)
You see, I understand that part. What I don't understand is how I can be moved away from a direction that the center of the Earth is moving and then back towards that direction and keep going that way if the Earth stopped rotating but kept moving the same way otherwise. It seems to me that I would remain still relative to the surface of the Earth.
I'm having a little trouble parsing your question, so instead of answering it directly, I'll describe what would happen and let you extract the exact answer you're looking for.
With the Earth rotating, you're always moving relative to the center of the Earth (unless you're at one of the poles). However quickly the surface of the Earth is rotating around its center, you're rotating around the Earth's center at the exact same speed. Since you, the Earth's surface, and everything around you are moving at this same speed, it looks like you're standing still from your perspective. Gravity keeps you stuck to the ground, while friction with the ground and air keep your speed matched to that of whatever part of the surface you're standing on. If you're standing still, the frictional force from the ground is minimal, so gravity is what accelerates you "away from the direction that the center of the Earth is moving and then back towards that direction" over the course of a day. The reason it can pull you first one way and then another is because as you follow the Earth's surface around its rotation, your position relative to the center of the Earth (and therefore the direction of gravity) is constantly changing.
If the Earth suddenly stopped rotating, you would still be moving at the same speed relative to the center of the Earth as you were before; that's Newton's 1st law of motion. You would suddenly find yourself (and anything else nearby that wasn't nailed down) flying off to the East, in the direction the Earth was rotating moments before. As you tumbled across the ground and ran into boulders and whatnot, various frictional and normal forces would slow you down until you once again came to rest relative to the surface. At this point, it would once again look like you were standing still from your perspective. However, you would no longer be moving around the Earth in circles, so gravity would no longer speed you up and slow you down relative to the Earth's direction of travel over the course of a day. You would just be moving with the same velocity as the center of the Earth all the time.
You see, I understand that part. What I don't understand is how I can be moved away from a direction that the center of the Earth is moving and then back towards that direction and keep going that way if the Earth stopped rotating but kept moving the same way otherwise.
It seems to me that I would remain still relative to the surface of the Earth.
You asked what would happen if the Earth suddenly stopped rotating, but continued to move otherwise. Thus you would lose your rotational component of motion but no others. You would come to "rest" on a non-rotating Earth still carrying the same velocity vector that the Earth carries.
Once you came to a stop, correct. However both you and the Earth would still be moving relative to other objects (like the Sun.)
jiveabillion: it's simpler than you think. See this website. The centre of the Earth is moving at 69,360.73 mph relative to the Sun in a circular fashion. But relative to the centre of the Earth, the surface at the equator is moving at 1041.7 mph in a circular fashion. If the Earth somehow instantaneously stopped spinning, you'd still be instantaneously moving at 69,360.73 mph relative to the Sun AND at 1041.7 mph relative to the centre of the Earth. Which is now motionless with respect to the surface. You can add these numbers together or subtract from the other, depending on whether you were on the day side or the night side; and variations in between. But whatever which way, you still end up moving at 1041.7 mph relative to the surface of the Earth.
Not good.
This is almost what I mean. Would I come to a stop before I hit something
or does the Earth's rotation make me actually move faster than the center of the Earth and I would go faster than the Earth in whatever direction that was tangent to its rotation when it stopped rotating?
No, every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.If I was standing on a trap door and, without gravity, would I still "fall" through it if it opened since there is nothing beneath me for the Earth to continue to push me with?
No, every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.
Like gmilam said, no. It's only like you're standing next to an ordinary door and I open it inwards.If I was standing on a trap door and, without gravity, would I still "fall" through it if it opened since there is nothing beneath me for the Earth to continue to push me with?