# Calculate the change of angular velocity

• SpaceThoughts
In summary, if you have a demonstration apparatus with two masses and you rotate it, you can calculate the final angular speed by knowing the initial angular speed and the moment of inertia of the structure.
SpaceThoughts
Hi there ...

How do I calculate the change of angular velocity, when demonstrating conservation of angular momentum?
I mean the change of angular velocity depends on the ratio between the two (rotating) masses that moves a distance along radius, and the (rotating) mass of the system itself.
In other words, if I know all the data about a rotating system before the change, could I possible figure out everything about the system after the changes just by knowing the distance traveled by the masses that moves along radius?
Is this at all possible to calculate?

I am not at university level, and would appreciate an easy to understand answer.

SpaceThoughts said:
Summary:: How do I calculate the change of angular velocity, when demonstrating conservation of angular momentum.
Just by knowing all the start data plus the distance traveled by the masses that moves along radius?

Hi there ...

How do I calculate the change of angular velocity, when demonstrating conservation of angular momentum?
I mean the change of angular velocity depends on the ratio between the two (rotating) masses that moves a distance along radius, and the (rotating) mass of the system itself.
In other words, if I know all the data about a rotating system before the change, could I possible figure out everything about the system after the changes just by knowing the distance traveled by the masses that moves along radius?
Is this at all possible to calculate?

I am not at university level, and would appreciate an easy to understand answer.

Could you describe the scenario you have in mind? What you've written doesn't make a lot of sense to me.

PeroK said:
Could you describe the scenario you have in mind? What you've written doesn't make a lot of sense to me.
When for example someone is demonstrating the conservation of angular momentum, switching between two different rotations. If I only know the data of the one rotation scenario, and decide a distance to move the masses along radius, will I then be able to calculate the new resulting rotation? With respect to the ratio between the mass of the system itself versus the mass of the two masses moved along radius.

SpaceThoughts said:
When for example someone is demonstrating the conservation of angular momentum, switching between two different rotations. If I only know the data of the one rotation scenario, and decide a distance to move the masses along radius, will I then be able to calculate the new resulting rotation? With respect to the ratio between the mass of the system itself versus the mass of the two masses moved along radius.

I can't follow that, I'm sorry to say. What rotations, what masses, what radius? What new resulting rotation?

You apparently have a specific piece of demonstration equipment in mind, but we are not understanding what this equipment looks like or what you are doing with it. Could you post a diagram and ask your question using the diagram as a reference?

That being said, it sounds like you have an apparatus consisting of a rotating structure and two masses on the rotating structure. While the device is spinning the two masses can be moved inward or outward closer to or further away from the axis of rotation. If I am understanding correctly, you want to know how to calculate the final angular speed after moving the masses given the initial speed and some knowledge of the moment of inertia of the structure and the mass of the weights.

If I have that right, this should be a very simple calculation. You will need to know the moment of inertia of the structure. Usually this is a simple disk shape so that the inertia is easily calculated, or it is provided by the manufacturer of the demonstration equipment. Moments of inertia add, so with the added masses the total moment of inertia is:

##I_{struct} + m_1 r_1^2 + m_2 r_2^2 ##

Often the masses have the same mass and are arranged so that they are always at the same distance from the axis. Then the inertia reduces to

##I_{struct} + 2 m r^2##

The position of the masses r is what you are changing, and this in turn changes the moment of Inertia

##I_{initial} = I_{struct} + 2 m r_{initial}^2##

Is changed to

##I_{final} = I_{struct} + 2 m r_{final}^2##

Assuming negligible friction, momentum is conserved:

##I_{initial} {\omega}_{initial}= I_{final} {\omega}_{final}##

SpaceThoughts
This is a really fine answer. Thanks a lot, it moves me forward ...

## 1. What is angular velocity?

Angular velocity is a measure of how fast an object is rotating around a fixed point. It is typically measured in radians per second (rad/s) or degrees per second (deg/s).

## 2. How do you calculate the change of angular velocity?

The change of angular velocity can be calculated by dividing the change in angular displacement by the change in time. This can be represented by the formula: Δω = Δθ / Δt.

## 3. What is the unit of measurement for angular velocity?

The unit of measurement for angular velocity can vary depending on the system of measurement being used. In the SI system, it is measured in radians per second (rad/s). In the imperial system, it is measured in degrees per second (deg/s).

## 4. How is angular velocity different from linear velocity?

Angular velocity measures the rate of change of angular displacement, while linear velocity measures the rate of change of linear displacement. Angular velocity is a vector quantity, meaning it has both magnitude and direction, while linear velocity is a scalar quantity, only having magnitude.

## 5. What factors can affect the change of angular velocity?

The change of angular velocity can be affected by factors such as the mass and shape of the object, the distance from the axis of rotation, and any external forces acting on the object. Additionally, the moment of inertia, which is a measure of an object's resistance to rotational motion, can also impact the change of angular velocity.

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