Please explain each response to each prompt using physics terms/ideas/formulas/proofs. I would like to check my own work. Please NO REPOSTS of other work.

"Centrifugal force." When you are in a car going around a sharp turn, you feel like there is some force pushing you sideways. Some people call this apparent force the centrifugal force, but as we have emphasized, this isn't some new force of nature. It's an apparent force that shows up because the system is not in an inertial reference frame (a frame that is not accelerating). Your body wants to move in a straight line due to its inertia, but the car is turning a corner and applies some combination of a normal force and friction you to keep you moving with the car. Remember Newton's second law: In an inertial reference frame, the acceleration of an object, a, is proportional to the net external force, Fnet = _ Fext, acting upon it, and the constant of proportionality is its mass, m. Namely, Fnet = ma. If the reference frame is accelerating, then Newton's law isn't accurate, and additional "forces" called inertial forces, may appear to act on the objects. It's very important to remember that these aren't actual forces, and should not be shown when drawing Force Diagrams in our usual inertial reference frames. We discuss them now to hopefully clarify some intuition that people generally carry with regard to non-inertial reference frames. (a) We're used to finding the centripetal acceleration (or force) for a mass moving in uniform circular motion in terms of its tangential speed and the radius of the circle. Write the apparent centrifugal force that appears to push radially outward in terms of the angular speed w and radius. This is very similar to other problems we've done, such as the g-force problem above. It's just a different perspective of circular motion. (b) A centrifuge is a common device in labs for biology, chemistry, biochemistry, and medicine that separates the components of a liquid or suspension by spinning a sample around at very high speed (and acceleration). You could say it applies a strong centrifugal force to the sample, forcing dense components out of a liquid, like separating the iron-rich red blood cells from blood plasma. What is the apparent acceleration felt by the sample at the bottom of the tube that is 8 cm from the axis of rotation and spinning at 15,000 rpm