DVDs hold approximately seven times more information and spin faster than CDs$.$ The angular speed of a DVD at the outer position, Point A in the image below, goes at $580$ RPM when it is being read. Just like the CD the "read head" passes the same length at all times and radii meaning the constant linear velocity $($CLV$)$ is why a DVD spins at various angular speeds. The information on these pits is read by lasers and is contained between $2\mathrm{.}5$ cm $($Point B$)$ and $5\mathrm{.}5$ cm $($Point A$)$ along a radial line.

a$.$ What is the tangential speed of any point on the DVD when it is being read by the laser?

b$.$ What is the angular speed when the inner position $($Point B$)$ is being read by the laser?

c$.$ If the DVD starts being read on the outside at Point A and is read continuously to the inside at Point B$,$ what is the magnitude of the average angular acceleration of the DVD$?$

d$.$ If the DVD rotates $92500$ times while it is being read, what is the running time of this movie?

e$.$ What is the average spacing between the lines of information?

f$.$ What is the tangential speed of the outer position at Point A when the laser is reading the inner position at Point B$?$

g$.$ What is the average tangential acceleration of the outer position at Point A during the playing of the DVD$?$