DVD Drive A DVD drive has a maximum speed of 7200...

DVD Drive A DVD drive has a maximum speed of 7200 revolutions per minute. If a DVD has a diameter of $12 \mathrm{~cm}$, what is the linear speed, in $\mathrm{km} / \mathrm{hr}$, of a point $5 \mathrm{~cm}$ from the disc's center if it is spinning at a rate of 5400 revolutions per minute?

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Key Concepts

Angular Velocity

Angular velocity describes the rate at which an object rotates or spins, typically measured in radians per second. It is a central concept in rotational motion, and converting from revolutions per minute (RPM) to radians per second provides the basis for analyzing how rotation affects points at various radii on a disc.

Relationship Between Angular and Linear Speed

This concept explains that the linear speed of a point on a rotating body is directly proportional to both the angular velocity and the distance from the center of rotation. In practical terms, a point farther from the center travels faster in a linear sense than a point closer to the center, as it covers a larger arc length per unit time.

Circumference of a Circle

The circumference of a circle, given by the formula 2?r, represents the distance a point at a fixed radius travels in one complete revolution. This concept is essential when relating the number of revolutions per minute to the linear distance traveled by a point on the circle.

Unit Conversion

Unit conversion is critical in problems involving different measurement systems. It involves translating values from one set of units to another—such as converting centimeters to kilometers and minutes to hours—to ensure that the final answer is expressed in the desired units, like kilometers per hour.

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