Vulcan: Now, find the tallest cliff, jump off it, you do not suddenly speed away from the cliff even though in theory "1000mph" rotational speed at the top is higher than the speed at the bottom.
Not speed away, no - you would move slightly to the east. The top of the cliff has greater linear velocity than the bottom.
If you stand on top of a 1000 ft cliff, you are doing extra ~6280 feet with every revolution of the Earth compared to the sea level.
A top of a cliff as high as the Earth's radius would be moving twice as fast as it's bottom.
The gravity would pull you straight down but your 1000mph horisontal velocity relative to the bottom would not go anywhere.
miko