# Doubts on angular momentum [master's degree exam]

• Raphael M
In summary: The moment of inertia of a hollow sphere about an axis through its center is 2/3 MR^2. The moment of inertia of a hollow sphere about an axis through its center is (2/3)(MR^2) + MR^2 = (8/3) MR^2.In summary, the system consists of two hollow spheres with mass and radius R, rotating around a center of mass with an initial period To. They are kept distant by an ideal wire with a distance of 8R. A motor is driven to make the spheres meet, with the inertia moment of the motor negligible and disregarding the effects of gravity. The angular momentum of the spherical shell is 2/3 MR^2. The
Raphael M
Homework template is missing; originally posted in non-homework forum
Two hollow spheres, both the mass and radius R M , which are rotating around a center of mass ( CM ) , with an initial period To, are kept distant from each other by an ideal wire with a distance of 8R. At a given instant a motor is driven by wrapping the wire and making the two spheres meet. Consider the inertia moment motor despicable , and disregard the effects of gravity . Express all your results in terms of M, R and To. Consider the angular momentum of the spherical shell 2 / 3MR2

a) determine the angular momentum of the system relative to the center of mass of time before the engine is started .

b ) determining the angular velocity of rotation at the time when a ball contacts the other
I Solved the a) like this

L = I.w
L = (2/3 MR²) . (2π(4R))/T0.(4R)
L = (4/3 MR²)/ T0

that's the angular momentum for 1 shell. multiply that by 2 to get the angular momentum to the sistem.

L = (8/3 MR²)/T0

But I can't solve the B part. I've tried everything I could, but I can't make the angular velocity at the contact situation in terms of T0.Help please ;)...
sorry about my english. I'm not fluent.

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Raphael M said:
I Solved the a) like this

L = I.w
L = (2/3 MR²) . (2π(4R))/T0.(4R)
L = (4/3 MR²)/ T0
You need the moment of inertia of each sphere about the axis of rotation. Use the parallel axis theorem.

## 1. What is angular momentum and how is it calculated?

Angular momentum is a physical quantity that measures the rotational motion of an object. It is calculated by multiplying the mass of an object by its velocity and its distance from the axis of rotation, known as the moment of inertia. The formula for angular momentum is L = I * ω, where L is angular momentum, I is moment of inertia, and ω is angular velocity.

## 2. What is the conservation of angular momentum?

The conservation of angular momentum states that the total angular momentum of a closed system remains constant, meaning it does not change over time. This means that if there are no external torques acting on an object, its angular momentum will remain constant.

## 3. How is angular momentum related to rotational motion?

Angular momentum is directly related to rotational motion because it measures the amount of rotational motion an object possesses. In fact, it is often referred to as the "rotational equivalent" of linear momentum. Just as linear momentum is conserved in linear motion, angular momentum is conserved in rotational motion.

## 4. What is the difference between angular momentum and linear momentum?

The main difference between angular momentum and linear momentum is the type of motion they describe. Angular momentum is related to rotational motion, while linear momentum is related to linear motion. Additionally, angular momentum takes into account an object's mass and its distance from the axis of rotation, while linear momentum only considers an object's mass and velocity.

## 5. How is angular momentum used in real-world applications?

Angular momentum has many practical applications in the real world. It is used in fields such as engineering, physics, and astronomy to understand and analyze rotational motion. It is also used in everyday objects such as gyroscopes, which use angular momentum to maintain stability and balance. In addition, the conservation of angular momentum is used in space missions to conserve fuel and maintain spacecraft orientation.

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