Conservation of angular momentum problem

In summary, the conversation discusses the violation of the law of conservation of energy in a scenario involving a clay and a rod. The clay has a kinetic energy of 5J, but one of the answers suggests that the initial rotational kinetic energy of the system is only 2J. This raises questions about where the missing 3J of energy goes. It is explained that in this type of inelastic collision, some energy is lost as random internal energy and deformation. This is similar to dropping a lump of clay onto the floor. The conversation then explores the concept of conservation of momentum and concludes that while (angular) momentum is always conserved, energy can be transformed into other forms but the sum is still conserved. It is also mentioned
  • #1
abro
20
0
I have been busy with rotating objects and I have a question which I don't understand. http://dev.physicslab.org/Document.aspx?doctype=3&filename=RotaryMotion_AngularMomentum.xml (last question of the page, about the clay on the rod)
What I don't understand is that the clay has a kinetic energy of KE=0,5*0,1*10^2=5J, but then one of the answers say the initial rotational kinetic energy, and thus the total energy of the system, is 2J. This is a violation of the law of conservation of energy. Please help?
 
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  • #2
abro said:
This is a violation of the law of conservation of energy. Please help?
The clay makes an inelastic collision with the rod (they stick together). Mechanical energy is not conserved.
 
  • #3
But where does the 3J go?
 
  • #4
abro said:
But where does the 3J go?
Random internal energy, deformation... things like that. (Things get warm.)

Drop a lump of clay onto the floor. It goes splat. What happened to its kinetic energy? Same idea.
 
  • #5
What about a solid ball that's sticky or something, will it suddenly get 3J of just because it hits a hanging rod with 5J?
 
  • #6
abro said:
What about a solid ball that's sticky or something, will it suddenly get 3J of just because it hits a hanging rod with 5J?
* get 3J of heat
 
  • #7
abro said:
What about a solid ball that's sticky or something, will it suddenly get 3J of just because it hits a hanging rod with 5J?
The collision takes some time. But yes, the system loses mechanical energy; that lost energy will show up as "heat" and other forms of "random" energy.
 
  • #8
Doc Al said:
The collision takes some time. But yes, the system loses mechanical energy; that lost energy will show up as "heat" and other forms of "random" energy.

Aha, there is also a familiar example with the conservation of moment, called the ballistic pendulum problem.
In conclusion; (angular) momentum is always (!) conserved, but energy can be transformed into other forms of energy, but the sum is also conserved.?
 
  • #9
abro said:
In conclusion; (angular) momentum is always (!) conserved, but energy can be transformed into other forms of energy, but the sum is also conserved.?
That's right. Angular momentum is conserved in such problems because there is no external torque acting. (The pivot is frictionless.)
 
1.

What is the conservation of angular momentum problem?

The conservation of angular momentum problem is a principle in physics that states that the total angular momentum of a closed system remains constant over time. This means that the angular momentum of a system cannot be created or destroyed, but can only be transferred between different objects or particles within the system.

2.

Why is the conservation of angular momentum important?

The conservation of angular momentum is important because it is a fundamental law of nature that governs the behavior of rotating objects. It helps explain many observed phenomena, such as the stability of rotating bodies and the motion of planets in our solar system. It also has practical applications, such as in spacecraft navigation and the design of turbines.

3.

How is angular momentum conserved in a system?

Angular momentum is conserved in a system when there is no external torque acting on the system. This means that the net torque on the system is equal to zero, and the total angular momentum remains constant. If an external torque is applied, the system's angular momentum will change, but the total angular momentum of the system and its surroundings will remain constant.

4.

What are some examples of the conservation of angular momentum in action?

One example of the conservation of angular momentum is the motion of a spinning top. As the top spins, its angular momentum remains constant, even as its axis of rotation may change. Another example is the motion of a skater performing a spin. By bringing their arms closer to their body, the skater decreases their moment of inertia and increases their angular velocity, demonstrating the conservation of angular momentum.

5.

Are there any exceptions to the conservation of angular momentum?

There are a few situations where the conservation of angular momentum does not hold true. One example is when an external torque is applied to a system, causing its angular momentum to change. Another is the behavior of quantum particles, where the principle of uncertainty allows for small changes in angular momentum. However, for most observable phenomena, the conservation of angular momentum remains a valid and useful principle.

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