# Circular motion ultra-centrifuge spin

• Jabababa
In summary, an ultra-centrifuge has a cylindrical disk that spins about an axis through its centre at an angular speed of 4.50 x 10^5 rad/s. When the driving force is turned off, the spinning slows down at a rate of 0.390 rad/s^2 due to air resistance. To determine how long the rotor spins before coming to rest, the formula Vf= Vi + at can be used, with the analogs of d → θ ; v → ω ; a → ##\alpha##. To find the initial linear speed of a point on the outer edge of the disk (26.0 cm in diameter), the formula v = ωr can be used. The initial radial

## Homework Statement

An ultra-centrifuge has a cylindrical disk mounted on an axle that is almost frictionless. The disk spins about an axis through its centre as shown. If the disk is spinning with an angular speed of 4.50 x 10^5 rad/s and the driving force is turned off, its spinning slows down (due to air resistance) at a rate of 0.390 rad/s^2.

a) How long does the rotor spin before coming to rest?

b) during the time that it is slowing down, how many revolutions does the rotor spin before coming to rest?

c) If the disk has a diameter of 26.0 cm, find the initial linear speed of a point on the outer edge of the disk.

d) find the magnitude of the initial radial acceleration of a point on the outer edge of the disk when it first starts to slow down.

e) find the magnitude of the initial tangential acceleration of a point on the outer edge of the disk when it first starts to slow down.

## The Attempt at a Solution

a) Vf= Vi + at => t = Vf-Vi/a

is that correct? I will start off with 1st one, and will add the work i did on b-e. If someone can let me know if that is correct. If wrong please explain what i did wrong.

Jabababa said:

## The Attempt at a Solution

a) Vf= Vi + at => t = Vf-Vi/a

is that correct? I will start off with 1st one, and will add the work i did on b-e. If someone can let me know if that is correct. If wrong please explain what i did wrong.

You will be better off working with the angular measures for this problem. The same formula can be applied to the angular measures by recognizing the analogs: d → θ ; v → ω ; a → ##\alpha##.

Other than the variables, am i on the right track?

try it and see ... starting calculation without being sure you are on the right track is good practice.

you can check also your reasoning ... the situation involves constant deceleration - that sort of motion has a special name.

if you are uncertain about equations, try deriving them from a ##\small \omega## vs t graph.

Jabababa said:
Other than the variables, am i on the right track?

You are, but it's a little early in the game to tell where the track might lead

Show some more work and a result.

## 1. What is a circular motion ultra-centrifuge spin?

A circular motion ultra-centrifuge spin is a scientific technique used to separate and purify substances based on their density differences. It involves spinning a sample at high speeds in a centrifuge, causing the denser particles to move towards the outside of the centrifuge and the less dense particles to stay closer to the center.

## 2. How does a circular motion ultra-centrifuge spin work?

A circular motion ultra-centrifuge spin works by creating a strong centrifugal force that pushes the particles in a sample towards the outside of the centrifuge. This force is created by spinning the sample at high speeds, causing the denser particles to move outwards and settle at the bottom of the sample tube.

## 3. What are the applications of circular motion ultra-centrifuge spin?

Circular motion ultra-centrifuge spin is commonly used in scientific research and industries such as pharmaceuticals, biotechnology, and chemistry. It is used to separate different components of a sample, such as cells, proteins, and DNA, for further analysis or purification.

## 4. Are there any safety concerns when using a circular motion ultra-centrifuge spin?

Yes, there are some safety concerns when using a circular motion ultra-centrifuge spin. The high speeds and forces involved can be dangerous if not used properly, so it is important to follow safety protocols and wear appropriate protective gear when operating the centrifuge.

## 5. Are there any limitations to circular motion ultra-centrifuge spin?

Yes, there are some limitations to circular motion ultra-centrifuge spin. The technique is most effective for separating particles with large density differences, and it can be difficult to separate particles that are similar in density. Additionally, the shape and size of the particles can also affect the separation process.