91Ó°ÊÓ

The concept of centripetal acceleration is crucial when studying objects moving in a circular path. It is the acceleration directed towards the center of the circle that keeps an object moving along the circular path. Even if the speed is constant, the velocity is not, because velocity is a vector and has both magnitude and direction. In this exercise, the centripetal acceleration is critical to determining the speed at which a centrifuge must spin to apply the necessary force to separate blood cells.

Using the formula for centripetal force, which is expressed mathematically as \( F = m \times a \), where \( F \) represents the force, \( m \) stands for the mass of the object, and \( a \) symbolizes the centripetal acceleration. From the given values, we ascertain the centripetal acceleration by rearranging the formula as \( a = F/m \). The resulting acceleration indicates how sharply the blood cell is changing its velocity, aiming towards the center of the centrifuge's path.

Angular velocity relates to objects moving in a circular path and measures how fast an object rotates or revolves relative to another point, usually the center of a circle. It is quantified as an angle rotated per unit time and is typically expressed in radians per second (rad/s). In our context, angular velocity is related to centripetal acceleration through the formula \( a = \omega^2r \), where \( \omega \) is the angular velocity, and \( r \) is the radius of the circular path.

In the given exercise, finding the angular velocity (\( \omega \)) allows us to understand how fast the centrifuge spins. After computing the centripetal acceleration, we can rearrange the formula to \( \omega = \sqrt{a/r} \), giving us the angular velocity in radians per second based on the calculated acceleration and the radius of the centrifuge. This value is a significant step in determining the operational speed for the centrifuge that influences the separation process of the blood cells.

The term 'revolutions per second' is a measure of rotational speed commonly used to describe how many complete turns an object makes in one second. It is directly related to the angular velocity but expressed in units of cycles or revolutions, which can be more intuitive. To convert from radians per second to revolutions per second, we divide the angular velocity by \(2\pi\), as there are \(2\pi\) radians in one full revolution.

From the solution provided, we understand how this conversion is applied, \( \omega / 2\pi = 10.623 \text{ rev/s} \). This final value is crucial in a practical setting when we control the centrifuge; it provides an easy-to-understand number that the equipment can be set to, ensuring the correct force is applied to efficiently separate the blood cells from the plasma in the sample. This conversion facilitates the usage of centrifuges, as their operational settings often require input in revolutions per minute (RPM) or per second.