A gyroscope consists of a rotating disk with a 25 cm radius suitably mounted at the midpoint of a 20 cm long axle so that it can spin and precess freely. One end is supported by a stand. The disk spins at 2000 rpm. The mass of the disk is 2 kg, and the axle can be taken as massless. Required:
a. Draw the gyroscope, indicating the direction of the initial angular speed and the initial angular momentum. Choose a direction for the spin of the disk.
b. Draw the torque due to gravity about the support point.
c. What direction will your gyroscope precess once you release it?
d. Find the time required for one precession of the gyroscope if it is supported at one end of the axle and it precesses in the horizontal plane.

A)  attached below

B) attached below

C) Anti-clockwise

D) 3.27 secs

Explanation:

A) Diagram of the gyroscope indicating direction of

attached below

B) Diagram of torque due to gravity about support point

Attached below

C) The direction the gyroscope will precess is ANTICLOCKWISE

D) Time required for one precession of the gyroscope

 use the relation below

MgL = ΔIw / Δt  

∴ Δt = ΔIw / MgL

       =( 1/2 * 2 * 0.25^2 * 2π * 2000 ) / ( 2 * 10 * 0.2 * 60 )

       = 3.27 secs

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.