To solve the problem, it is necessary to apply the concepts related to the kinematic equations of the description of angular movement.
The angular velocity can be described as

Where,
Final Angular Velocity
Initial Angular velocity
Angular acceleration
t = time
The relation between the tangential acceleration is given as,

where,
r = radius.
PART A ) Using our values and replacing at the previous equation we have that



Replacing the previous equation with our values we have,




The tangential velocity then would be,



Part B) To find the displacement as a function of angular velocity and angular acceleration regardless of time, we would use the equation

Replacing with our values and re-arrange to find 



That is equal in revolution to

The linear displacement of the system is,



The speed of light to be slightly less in atmosphere then in vacuum because of absorption and re-emission of light by the atmospheric molecules occurred when light travels through a material
<u>Explanation:</u>
When light passes through atmosphere, it interacts or transmits through the transparent molecules in atmosphere. In this process of transmission through atmosphere, the light will be getting absorbed by them and some will get re-emitted or refracted depending upon wavelength.
But in vacuum the absence of any kind of particles will lead to no interaction and no energy loss, thus the speed of the light will be same in vacuum while due to interactions with molecules of atmosphere, there speed will be slightly less compared to in vacuum.
Let s = rate of rotation
<span>Let r = radius of earth = 6,400km </span>
<span>Then solving (s^2) r = g will give the desired rate, from which length of day is inferred. </span>
<span>People would not be thrown off. They would simply move eastward in a straight line while the curved surface of earth fell away from beneath them.</span>