A compact disc (CD) player varies the rotation rate of the...

A compact disc (CD) player varies the rotation rate of the disc in order to keep the part of the disc from which information is being read moving at a constant linear speed of $1.30 \mathrm{m} / \mathrm{s}$ Compare the rotation rates of a 12.0 -cm-diameter CD when information is being read (a) from its outer edge and (b) from a point $3.75 \mathrm{cm}$ from the center. Give your answers in $\mathrm{rad} / \mathrm{s}$ and rpm.

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Key Concepts

Relationship between Linear and Angular Velocity

This concept describes how the linear speed (v) of a point on a rotating object is directly proportional to both the angular speed (?) and its distance (r) from the axis of rotation, given by the equation v = ?r. It is fundamental in circular motion analysis, allowing one to determine the effect of changing radius on the rotation rate when maintaining a constant linear speed.

Conversion between Angular Velocity Units

Understanding this concept involves converting between different units of angular velocity, such as radians per second and revolutions per minute (rpm). Since one complete revolution is 2? radians and there are 60 seconds in a minute, this conversion is essential for interpreting and comparing rotational speeds in various contexts.

Circular Motion

Circular motion is the study of objects that move along curved paths, particularly circles. It involves analyzing how forces, speeds, and radii interact to produce rotational dynamics. This concept provides the framework for understanding the behavior of systems where maintaining a constant linear speed along a circular path is required.

Transcript

00:01 I wrote down the pertinent information for you, but i want to read the question.

00:06 A cd player varies the rotation rate of a disc in order to keep the part of the disc from which information is being read moving at a constant linear speed of 1 .30 meters per second.

00:21 So i wrote that down.

00:23 Compare the rotation rates of a 12 centimeter diameter cd.

00:28 Well, 12 centimeters diameter is going to.

00:31 Going to give us six centimeters radius.

00:34 So that's why i wrote down six.

00:37 When information is being read, a from the outer edge.

00:42 So at the outer edge, the radius is six.

00:47 And we know that omega equals v over r.

00:51 So omega equals v, which is 1 .30 meters per second, divided by r, which is 0 .06 meters.

01:07 So we just put that in a calculator.

01:10 1 .3 divided by 0 .06.

01:16 1 .3 divided by 0 .06 gives us to three significant digits 21 .7 radiance per second.