A uniform disk with mass 38.7 kg and radius 0.240 m is pivoted at its center about a horizontal, frictionless axle that is stationary. The disk is initially at rest, and then a constant force 30.0 N is applied tangent to the rim of the disk. What is the magnitude v of the tangential velocity of a point on the rim of the disk after the disk has turned through 0.320 revolution?

Explanation:

Given:

mass of uniform disk, radius of the disk, initial velocity of the disk, magnitude of the force acted upon the rim of the disk, angular displacement of the disk,

Moment of inertia of the given disk:

Also the torque due to the force is given as:

Torque in terms of angular acceleration:

where:

angular acceleration

Now using the equation of motion:

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.