The platter of the hard drive of a computer rotates at 7200 rpm (rpm = revolutions per minute = rev/min). What is the angular velocity (rad/s) of the platter?

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Convert the given rotational speed from revolutions per minute (rpm) to revolutions per second (rps). Use the relationship: 1 minute = 60 seconds. The formula is: \( \text{rps} = \frac{\text{rpm}}{60} \).

Recognize that one revolution corresponds to an angular displacement of \( 2\pi \) radians. To find the angular velocity in radians per second (rad/s), multiply the revolutions per second (rps) by \( 2\pi \). The formula is: \( \omega = \text{rps} \times 2\pi \).

Substitute the value of \( \text{rps} \) from step 1 into the formula from step 2 to calculate \( \omega \), the angular velocity in rad/s.

Simplify the expression to express \( \omega \) in terms of \( \pi \) for clarity, if needed.

Ensure the units are consistent throughout the calculation and confirm that the final angular velocity is expressed in radians per second (rad/s).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Angular Velocity

Angular velocity is a measure of how quickly an object rotates around an axis, expressed in radians per second (rad/s). It quantifies the rate of change of angular displacement and is crucial for understanding rotational motion. The formula to convert from revolutions per minute (rpm) to radians per second is: angular velocity (ω) = (rpm × 2π) / 60.

Revolutions and Radians

A revolution refers to a complete turn around a circle, which corresponds to an angular displacement of 2π radians. Understanding the relationship between revolutions and radians is essential for converting angular measurements. This conversion is necessary when calculating angular velocity from rpm, as it allows for a consistent unit of measurement in physics.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In this context, converting rpm to rad/s involves understanding the relationship between the units and applying appropriate conversion factors. Mastery of unit conversion is vital in physics to ensure that calculations are accurate and meaningful across different contexts.

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The platter of the hard drive of a computer rotates at 7200 rpm (rpm = revolutions per minute = rev/min). If a single bit requires 0.50 μm of length along the direction of motion, how many bits per second can the writing head write when it is 3.00 cm from the axis?

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Textbook Question

The platter of the hard drive of a computer rotates at 7200 rpm (rpm = revolutions per minute = rev/min). If the reading head of the drive is located 3.00 cm from the rotation axis, what is the linear speed of the point on the platter just below it?

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