Problem 21 - College Physics

Question

What is the period of revolution for (a) a 9500-rpm centrifuge and (b) a 9500-rpm computer hard disk drive?

Step-by-Step Solution

Answer

The period of revolution is approximately 0.00632 seconds for both devices.

Step 1: Understanding Revolutions per Minute (RPM)

Revolutions per minute (RPM) is a measure of the number of complete turns a rotating object makes in one minute. Knowing the RPM allows us to determine the period, which is the time taken for one complete revolution.

Step 2: Convert RPM to Revolutions per Second (RPS)

Since period is usually calculated in seconds, we first convert revolutions per minute (RPM) to revolutions per second (RPS). For both the centrifuge and the hard disk drive: \[ 9500 ext{ RPM} = \frac{9500}{60} ext{ RPS} \]

Step 3: Calculate RPS

Perform the division to find revolutions per second:\[ \frac{9500}{60} \approx 158.33 ext{ RPS} \] Thus, both the centrifuge and the hard disk drive operate at approximately 158.33 revolutions per second.

Step 4: Find the Period of One Revolution

The period \( T \) of revolution is the reciprocal of the number of revolutions per second. Thus, \[ T = \frac{1}{ ext{RPS}} \] Substituting the values:\[ T = \frac{1}{158.33} \approx 0.00632 ext{ seconds} \]

Step 5: Conclusion

The period for one complete revolution of both the 9500-RPM centrifuge and the 9500-RPM computer hard disk drive is approximately 0.00632 seconds.

Key Concepts

Revolutions per Minute (RPM)

Revolutions per minute, or RPM, is an important concept that describes the speed of rotation. It tells us how many full turns an object completes in a minute. This unit of measurement is very common in various applications, like engines and hard drives.
When you understand an object's RPM, you can easily figure out its rotational behavior over time. RPM helps determine the period of revolution, which is the time taken to complete one full circle. Understanding this connection can be crucial when working with machinery, as it indicates how quickly or slowly an object is moving.
The formula that connects RPM to the period is straightforward. To find out how long it takes for one full turn, you first need to know the revolutions per second. This conversion makes calculations easier when dealing with time, as it aligns more closely with standard units of seconds.

Revolutions per Second (RPS)

Once we know the object's revolutions per minute, we can convert this to revolutions per second (RPS). This step is necessary because calculations involving time are often easier in seconds.
RPS gives you a more direct view of how quickly something turns within just one second. To find RPS from RPM, simply divide the number of revolutions per minute by 60, since there are 60 seconds in a minute.
For instance, in our example with the 9500 RPM centrifuge or hard drive, we divide 9500 by 60, which equals approximately 158.33 RPS.

• This simple conversion makes it easier to calculate time-dependent parameters, like the period of revolution.

Using RPS allows us to directly find out how often the object completes its cycle in the universally familiar unit of seconds, aiding in comprehensive analysis.

Physics Problem Solving

Solving physics problems often involves a step-by-step approach to understanding and calculation. This approach ensures all necessary information is considered to reach an accurate solution. Starting with known values, like RPM, is key.
After this, breaking down the problem into manageable steps, such as converting RPM to RPS, simplifies the task. The next main step is the calculation itself, which involves straightforward mathematics. For example, if we have 158.33 RPS, we can find the period using the formula:

• The formula for the period of revolution is: \[ T = \frac{1}{\text{RPS}} \]

Continuing with our example, by plugging RPS into the formula, we find that the period is approximately 0.00632 seconds.
This solution shows us how to apply mathematical methods to uncover key details about the object's motion. Through these careful calculations, we gain a clearer, mathematical snapshot of rotational motion in mechanical systems.