# Angular Momentum: Clarifying a Problem

• fro
Keep up the good work.In summary, the problem is about finding the angular momentum of a particle with a given mass, angular speed, and radius. The correct calculation for the rotational inertia is 0.0064 kg/m^2, and the angular momentum is 0.128 kg*m^2/s. However, the units for rotational inertia and angular momentum should be kg*m^2 and kg*m^2/s, respectively.
fro

Problem: A particle of mass 0.01kg rotates with angular speed of 2 rad/s in a circle of radius 0.8m. What is its angular momentum?

I think the answer should be:
I = 0.01kg X (0.8m^2) = 0.0064 kg/m^2.
Therefore, angular momentum = 0.0064 kg/m^2 X 2 rad/s = 0.128 kg*rad/m^2*s.

Am I on the correct path?

fro said:
I think the answer should be:
I = 0.01kg X (0.8m^2) = 0.0064 kg/m^2.
Therefore, angular momentum = 0.0064 kg/m^2 X 2 rad/s = 0.128 kg*rad/m^2*s.

You are correct in your calculations, but not in your units. The unit for rotational inertia is kg*m^2, which is what your math would indicate. Also, the radians are generally not included in the units for angular momentum, so you should come up with an answer in the form kg*m^2/s.

Your calculations appear to be correct. Angular momentum is a measure of an object's rotational motion and is calculated as the product of its moment of inertia (I) and angular velocity (ω). In this problem, the particle's moment of inertia is calculated using its mass and the distance from the axis of rotation (radius). The angular velocity, in this case, is given as 2 rad/s. Multiplying these two values gives the angular momentum, expressed in units of kg*rad/m^2*s. Therefore, your answer of 0.128 kg*rad/m^2*s is correct. If you are still unsure about the concept of angular momentum, I recommend reviewing some basic principles of rotational motion and practicing similar problems to solidify your understanding.

## What is angular momentum?

Angular momentum is a physical quantity that describes the rotational motion of a system. It is a vector quantity that combines an object's mass, velocity, and distance from the axis of rotation.

## How is angular momentum different from linear momentum?

Linear momentum describes an object's motion in a straight line, while angular momentum describes an object's motion around an axis. Linear momentum is a product of an object's mass and velocity, while angular momentum also takes into account the distance from the axis of rotation.

## What is the conservation of angular momentum?

The conservation of angular momentum states that angular momentum remains constant in the absence of external torques. In other words, the total angular momentum of a system before an interaction is equal to the total angular momentum after the interaction.

## How is angular momentum calculated?

Angular momentum is calculated by multiplying an object's moment of inertia (a measure of its resistance to rotation), its angular velocity (how fast it is rotating), and the distance from the axis of rotation.

## What are some real-world examples of angular momentum?

Some examples of angular momentum include the rotation of planets around the sun, the spinning of a top, and the movement of a gyroscope. Angular momentum is also important in sports, such as figure skating and gymnastics, where athletes use their body's rotation to perform complex movements.

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