# What is the angular velocity and kinetic energy of a cockroach-disk system?

• cd80187
In summary, the cockroach has a new kinetic energy of K after it walks halfway to the center of the disk. The new kinetic energy is K/K0 = 0.571.
cd80187
A cockroach of mass m lies on the rim of a uniform disk of mass 4.29m that can rotate freely about its center like a merry-go-round. Initially the cockroach and disk rotate together with an angular velocity of 0.271 rad/s. Then the cockroach walks halfway to the center of the disk. (a) What then is the angular velocity of the cockroach-disk system? (b) What is the ratio K/K0 of the new kinetic energy of the system to its initial kinetic energy?

I am not even sure how to begin this problem. I thought you could set up a ratio using v= r times omega. But that didn't work out, so I'm not sure where to even begin, even though the book says it relates to angular momentum.

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Consider conservation of angular momentum.

I figured it had something to do with that, but how am I supposed to figure out the rotational inertia, and for it, do i find the rotational inertic from the cockraoch using the parallel axis theorem and then add it to the rotational inertia of the disk, and then do it once again for the new placement of the cockraoch?

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I'm still having trouble figuring this one out

cd80187 said:
I figured it had something to do with that, but how am I supposed to figure out the rotational inertia, and for it, do i find the rotational inertic from the cockraoch using the parallel axis theorem and then add it to the rotational inertia of the disk, and then do it once again for the new placement of the cockraoch?
That will work. You can treat the cockroach as a point mass.

So should I treat it as a particle with it as its own axis, or should I still do the parallel axis theorem and count r as the distance between the cockraoch and the center?

Either way will give you the same answer. Try it and see.

## 1. What is angular velocity?

Angular velocity is a measure of the rate at which an object is rotating or turning. It is defined as the change in an object's angular displacement over time, and is typically measured in radians per second.

## 2. How is angular velocity measured?

Angular velocity can be measured using an angular velocity sensor, such as an accelerometer or gyroscope, which can detect changes in an object's rotation. It can also be calculated by dividing the change in angular displacement by the change in time.

## 3. Why is the angular velocity of cockroaches studied?

The angular velocity of cockroaches is studied because it can provide insights into their movement patterns and behavior. By understanding their angular velocity, scientists can better understand how cockroaches navigate and respond to their environment.

## 4. What factors affect the angular velocity of cockroaches?

The angular velocity of cockroaches can be affected by various factors, including the size and shape of their body, their muscle strength and coordination, and the terrain or environment in which they are moving.

## 5. Can the angular velocity of cockroaches be used for any practical applications?

Yes, the study of cockroach angular velocity has potential applications in fields such as robotics and biomimicry. By understanding how cockroaches move and navigate, scientists can develop more efficient and agile robots, or use their movements as inspiration for new technologies.

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