Need Help With Physics Question--Please help Math gods!?

Question

How much work is done by the motor in a CD player to make a CD spin, starting from rest? The CD has a diameter of 12.7 cm and a mass of 14.8 g. The laser scans at a constant tangential velocity of 1.22 m/s. Assume that the music is first detected at a radius of 19.5 mm from the center of the disk. Ignore the small circular hole at the CD's center?

The answer that the book has is 0.0584 J
How do "they" come up with that crazy number??

Answer 1

The energy of the disc spinning is .5*I*w^2. I=.5*M*Rd^2 (Rd = 12.7/2 cm). Angular velocity w = tangential velocity/Rl (Rl is 19.5mm). Just do the calcs, but be careful to keep the units straight (you have meters, cm and mm) The book has the right answer.

Answer 2

The work done is to add an angular momentum (via a torque) to accelerate the disk from rest to the specified speed. The trick is that the moment of inertia of a disk is equivalent to a mass situated at a distance part way between the center and the edge. The exact location can be determined by calculus, or by looking it up in a table. Checking my favorite table, the moment of inertia is mr*2/2. With that bit of wisdom, you should be able to work it out.

Answer 3

Radius of cd, R=6.35 cm = 6.35E-2 m
Mass M= 14.8 g = 14.8E-3 kg
Momemt of Inertia, I= 0.5* M*R^2
Angular velocity, w= 1.22/19.5E-3 radians/s
You are looking for the work done, which will be the kinetic energy given to the cd
=0.5* I*w^2= 0.06J
Simple isn't it!

BTW, the notation E refers to 10 power, * is multiplication and ^ is for exponent, in case you dont know.

Answer 4

In history, it style of feels that arithmetic and physics, not to show education at the instant are not yet universal. it style of feels that it replaced right into a era in general delivered approximately via mysteries, on condition that they are able to't be defined, or the right thank you to handle it fairly is unknown. artwork replaced into additionally the considerable emphasis of the "knowledgeable" and experienced back then. Ornate products like jars, carpets, silver/gold wares mattered extra effective than some guy's muttering. in my opinion, i think of math replaced into universal someplace in China and Greece interior the old days. examine different history books and you will see that "magic" replaced into in actuality an application of right this moment's physics and chemistry. Magic, miracles, super powers fairly do provoke people. yet once you get the carry close of it (know what it fairly is and the thank you to do it) it is going to become undemanding, even out of date.