Conservation of angular momentum

In summary, if a body is rotated with no external forces acting on it in the tangential direction, it will have angular momentum with respect to the axis of rotation. This angular momentum can be calculated using the equation Lo = Ro * Vo * m, where Ro is the initial radius of rotation, Vo is the initial tangential velocity, and m is the mass of the body. If the string is pulled in with respect to time and no torque is applied, the velocity can be calculated using V(t)=\frac{Vo*Ro}{r(t)} and the tangential acceleration can be calculated using a(t)=\frac{-Vo*Ro}{(r(t)^2)}*r(t)', where r(t)' is the derivative of
  • #1
MechatronO
30
1
Imagine a body that is attached to a massless string and then rotated in such a manner that no external forces like gravity acts on the body in tangential direction.

The body now has the angular momentum with respect to the axis of rotation

Lo = Ro * Vo * m

Where

Ro = constant initial radius of rotation
Vo = constant initial tangential velocity
m= mass of the body

If the string is pulled in with respect to time, and no torque is applied with respect to the axis of rotation would the velocity be this, according to the law about conservation of angular momentum?

V(t)=[itex]\frac{Vo*Ro}{r(t)}[/itex] ?



And would the tangential acceleration then be

a(t)=[itex]\frac{-Vo*Ro}{(r(t)^2)}[/itex]*r(t)' ?

Where

r(t)´ = the derivate of the radius of rotation with respect to time

If so, could this acceleration be added directly to external forces that is causing tangential acceleration?

The purpose is forwarding a regulator that will control the acceleration of a robot.
 
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  • #2
Looks right.
External forces could change r'(t), but if they do not, I would expect that you can add them.
 

What is conservation of angular momentum?

Conservation of angular momentum is a fundamental law of physics that states that the total angular momentum of a system remains constant if there are no external torques acting on the system. In other words, the rotational motion of a system will not change unless an external force is applied.

How is angular momentum defined?

Angular momentum is defined as the product of an object's mass, velocity, and distance from a fixed axis. Mathematically, it is represented as L = mvr, where L is angular momentum, m is mass, v is velocity, and r is the distance from the axis of rotation.

What are the types of angular momentum?

There are two types of angular momentum: orbital angular momentum and spin angular momentum. Orbital angular momentum is associated with the motion of an object around an external axis, while spin angular momentum is associated with the internal rotation of an object.

How does conservation of angular momentum apply to real-world situations?

Conservation of angular momentum has many real-world applications, such as in the motion of planets and satellites in our solar system, the motion of spinning tops and gyroscopes, and the motion of atoms and subatomic particles.

Can angular momentum be transferred between objects?

Yes, angular momentum can be transferred between objects through collisions or interactions. However, the total angular momentum of the system will remain constant, meaning that if one object gains angular momentum, another object must lose an equal amount.

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