# Angular momentum of a rotating disc

• LCSphysicist
In summary, the conversation discusses finding the angular momentum of a rotating disc relative to a stationary point, caused by the Coriolis force. The appropriate equation to start with is the cross product of the position and velocity vectors. The direction of the velocity v0 of the disc is not specified. To relate the Coriolis force to the angular momentum, one should find the torque in the rotating frame, and then find the position and velocity vectors as functions of time. The centrifugal force is not a good justification for the equation being equal to the Coriolis force. The section "Relation between the accelerations in the two frames" is recommended for solving the problem in the non-inertial frame.
LCSphysicist
Homework Statement
Torque
Relevant Equations
Coriolis force
"A smooth horizontal disc rotates with a constant angular velocity ω about a stationary vertical axis passing through its centre, the point O. At a moment t=0 a disc is set in motion from that point with velocity v0. Find the angular momentum M(t) of the disc relative to the point O in the reference frame fixed to the disc. Make sure that this angular momentum is caused by the Coriolis force."

How about being a bit more specific and make a bit more of an effort.
What is the appropriate relevant equation? "Coriolis force" is not an equation.
In what direction is the velocity v0 of the disc?
How would you proceed to relate the Coriolis force to the angular momentum of the disc? FInding the torque in the rotating frame is a good start. What do you think should come next to find M(t)?

Last edited:
etotheipi
kuruman said:
How about being a bit more specific and make a bit more of an effort.
What is the appropriate relevant equation? "Coriolis force" is not an equation.
In what direction is the velocity v0 of the disc?
How would you proceed to relate the Coriolis force to the angular momentum of the disc? FInding the torque in the rotating frame is a good start. What do you think should come next to find M(t)?

Do you think that starting with the angular momentum and then finding the torque is not a good idea? can the answer mislead me?
"What about the centrifugal force?" That's a good question, i just finished when i saw that the equation seems equal to the equation of coriolis force, but that's, indeed, is not a good justification.
I am trying to answer the other questions, its been hard to work in this reference frame.

LCSphysicist said:
Do you think that starting with the angular momentum and then finding the torque is not a good idea? can the answer mislead me?
Starting with the angular momentum is not a bad idea depending on what you do next. I would write ##\vec L(t)=m \vec r(t)\times \vec v(t)## first. Then I would find the position and velocity vectors as functions of time and form the cross product.
LCSphysicist said:
"What about the centrifugal force?" That's a good question, i just finished when i saw that the equation seems equal to the equation of coriolis force, but that's, indeed, is not a good justification.
I am trying to answer the other questions, its been hard to work in this reference frame.
You might find the section "Relation between the accelerations in the two frames" here extremely useful. All you have to do is pretend that in the non-inertial frame the fictitious forces are real and solve the appropriate differential equation to find the position and velocity as functions of time.

## 1. What is angular momentum?

Angular momentum is a physical quantity that describes the rotational motion of an object. It is a vector quantity that is defined as the product of an object's moment of inertia and its angular velocity.

## 2. How is angular momentum related to a rotating disc?

In a rotating disc, the angular momentum is directly proportional to the disc's moment of inertia and its angular velocity. This means that as the moment of inertia or the angular velocity increases, so does the angular momentum.

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

The conservation of angular momentum states that the total angular momentum of a system remains constant unless an external torque is applied. This means that in a closed system, the initial angular momentum will be equal to the final angular momentum.

## 4. How does the angular momentum of a rotating disc change when its speed changes?

According to the equation for angular momentum (L = Iω), as the angular velocity of a rotating disc changes, its angular momentum also changes. If the angular velocity increases, the angular momentum will increase and vice versa.

## 5. How can angular momentum be calculated for a rotating disc?

The angular momentum of a rotating disc can be calculated using the equation L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. The moment of inertia can be calculated using the mass distribution and the axis of rotation of the disc.

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