A5.0-m-diameter merry-go-round is initially turning with a 4.0 s period. it slows down and stops in 20 s. what is the angular acceleration as it stops.

First, we can find the initial angular speed of the merry-go-round. Calling the period of revolution, the initial angular speed is


Then, the merry-go-round starts to decelerate, so it is an angular accelerated motion with angular acceleration , and the angular velocity follows the law

We know that after t=20 s, the merry go round stops, so . So we can rewrite the previous equation and solve it to find :


where the negative sign means the merry-go-round is decelerating.

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by  mathematical calculations  before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of  uranus  led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to   spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.