# Calculating Angular Velocity of Disk w/ Angular Momentum

• srecko97
In summary, the question involves a man with mass 70 kg walking on a disk with a radius of 1.5 m and a speed of 4 m/s. The goal is to calculate the angular velocity of a disk with mass 200 kg and a radius of 2 m on which the man is standing. The equation used is angular momentum = J * w, where J is the moment of inertia and w is the angular velocity. The solution involves setting the angular momentum of the disk equal to the angular momentum of the man and solving for the angular velocity. However, the mistake made was in assuming that the velocity given (4 m/s) was the man's velocity towards the observer, when it actually referred to the man's
srecko97

## Homework Statement

There is a man walking on a disk with mass 70 kg and speed 4 m/s. He walks on a circle with radius 1,5 m. How fast does the disk (mass 200 kg and radius 2 m) under him rotates (need to calculate angular velocity)[/B]

## Homework Equations

angular momentum = J * w (J-moment of inertia, w, angular velocity)

## The Attempt at a Solution

(J_disk) * (w_disk) = (J_man) * (w_man)
1/2 MR^2 *(w_disk) = (mr^2* ( v_man)) / r
(w_disk) = mr(v_man) / MR^2
(w_disk) =1,05 /s

What am I doing wrong?

I have already solved it. It is so so easy (I knew that before, that is why I was asking here, as I was sure that my answer was correct). I did not see that it was written that the velocity (4m/s) meant the velocity of a man towards the disk, not towards the observer somewhere out of the disk.

## 1. How do you calculate the angular velocity of a disk?

The angular velocity of a disk can be calculated by dividing the angular momentum by the moment of inertia of the disk. The formula for angular velocity is ω = L/I, where ω is the angular velocity, L is the angular momentum, and I is the moment of inertia.

## 2. What is angular momentum and how is it related to angular velocity?

Angular momentum is a measure of the rotational motion of an object. It is the product of the moment of inertia and the angular velocity. In other words, it is the amount of rotational energy an object possesses due to its mass and speed of rotation. Angular velocity and angular momentum are directly proportional to each other, meaning that an increase in one will result in an increase in the other.

## 3. What is the moment of inertia of a disk?

The moment of inertia of a disk is a measure of how difficult it is to change the rotational motion of the disk. It depends on the mass and distribution of the mass within the disk. For a solid disk, the moment of inertia can be calculated using the formula I = ½mr², where m is the mass of the disk and r is the radius of the disk.

## 4. How is the angular velocity of a disk affected by changes in its moment of inertia?

The angular velocity of a disk is inversely proportional to its moment of inertia. This means that as the moment of inertia increases, the angular velocity decreases and vice versa. For example, if the mass of the disk increases, its moment of inertia also increases, resulting in a decrease in its angular velocity.

## 5. Can the angular velocity of a disk change?

Yes, the angular velocity of a disk can change. It can change if there is a change in the external torque acting on the disk or if there is a change in the distribution of mass within the disk. The angular velocity can also change if the moment of inertia of the disk changes, as discussed in the previous question.

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