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

Rotational Motion

Rotational motion involves the movement of an object around a central axis. In this context, the concept explains how the revolutions per minute (rpm) of a disc determine its angular velocity, which is essential for relating the rotational speed to the linear speed of a point on the disc.

Linear Velocity in Circular Motion

Linear velocity in circular motion is the speed at which a point on the rotating object travels along its circular path. This is determined by multiplying the angular speed (in radians per time unit) by the radius at which the point is located, connecting angular and linear measurements.

Circumference of a Circle

The circumference of a circle, given by 2? times the radius, represents the total distance a point travels in one complete revolution. This concept is critical for understanding how far a point moves over multiple rotations when calculating linear speed.

Unit Conversion

Unit conversion is the process of changing measurements from one unit to another to maintain consistency in calculations. In problems involving rotational and linear speeds, it is important to convert units—such as converting centimeters per minute to kilometers per hour—to express the final answer in the desired units.

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