You hold a bucket in one hand. in the bucket is a 500g rock. you swing the bucket so that the rock moves in a vertical circle 2.2m in diameter. what is the minimum speed the rock must have at the top of the circle if it is to always stay in contact with the bottom of the bucket?

An asteroid is discovered in a nearly circular orbit around the sun, with an orbital radius that is 2.47 times earth's. what is the asteroid's orbital period, its "year," in terms of earth years?

10 newton object is placed 3 meters from the fulcrum. at what distance on the other side would you need to place a 15 newton object to balance the lever? show your work!

Agroup of monkeys is trying to cross the river in a rowboat. the maximum buoyant force on the rowboat is 2,000 n. the weight of the rowboat is 1,000 n. each monkey has a weight of 150 n. how many monkeys can safely cross in the rowboat at one time? explain your reasoning, including any calculations you used to find the answer.