A Blu-ray drive has a maximum speed of 10,000 revolutions...

A Blu-ray drive has a maximum speed of 10,000 revolutions per minute. If a Blu-ray disc has a diameter of $12 \mathrm{~cm}$, what is the linear speed, in $\mathrm{km} / \mathrm{hr}$, of a point $4 \mathrm{~cm}$ from the center if the disc is spinning at a rate of 8000 revolutions per minute?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Circular Motion

Circular motion refers to movement along a circular path. In this context, every point on a rotating disc follows a circular path with a radius equal to its distance from the center. The tangential or linear speed of a point on the circle depends on both the angular speed of the disc and its distance from the center. This relationship is used to convert rotational motion into linear motion.

Angular Velocity

Angular velocity describes how quickly an object rotates and is typically expressed in radians per unit time. It can be derived from the number of revolutions per minute by recognizing that each revolution corresponds to 2? radians. This conversion is crucial for calculating linear speeds from rotational speeds using the formula v = ?r, where ? is the angular velocity and r is the radius.

Unit Conversion

Unit conversion involves changing measurements from one set of units to another to ensure consistency in calculations. In problems like this, it is necessary to convert angular speed from revolutions per minute to radians per second and linear distances from centimeters to kilometers, as well as converting time from seconds to hours. Effective unit conversion allows for the final answer, such as linear speed, to be expressed in the desired units of kilometers per hour.

Transcript

Please give Ace some feedback