Angular Velocity of Particle Rod System After Impact

In summary, the conversation discusses a mass colliding with a rigid rod that is attached to a frictionless hinge. The angular velocity of the particle rod system after impact is being determined. It is mentioned that the initial angular momentum is equal to the final angular momentum, and the formula for finding the final angular momentum is provided. The rotational inertia of the combined rod and mass is also discussed, and the final angular momentum is solved for by setting the initial and final angular momentum equal to each other.
  • #1
captainjack2000
99
0
1. A mass m is moving with velocity v. it then collids with the end of a rigid rod perpendicular to its intial path. They stick together. The other end of the rod is attached to a frictionless hinge which allows it to rotate in any direction. rod mass = M length = l
What is the angular velocity of the particle rod system after impact?

3. Initally the only angular momentum would be L = mvl
angular momentum is conserved so the intial L = final L
I am a bit confused about how to find the final L?
L=rmv
L = Iw(for the rod) +mwl for the particle?
I for the rod = MR^(2) / 3
 
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  • #2
Once they collide and stick together they become one body. What's the rotational inertia of "rod + mass"?
 
  • #3
Is it just I = (m+M)R^(2)
 
  • #4
captainjack2000 said:
Is it just I = (m+M)R^(2)
No. You already know the rotational inertia of the stick. Just add the rotational inertia of a point mass at its end.
 
  • #5
So the final angular momentum would equal
L = [Ml^(2) / 3]w + [Ml^2]w?
where w = vl?
 
  • #6
captainjack2000 said:
So the final angular momentum would equal
L = [Ml^(2) / 3]w + [Ml^2]w?
Almost. That second mass should be m, not M.
where w = vl?
No. (If that were true, you could just write down the answer!) Set initial angular momentum equal to final angular momentum and solve for w.
 

1. What is angular velocity?

Angular velocity is a measure of how fast an object is rotating around a central point. It is typically measured in radians per second.

2. How is angular velocity related to linear velocity?

Angular velocity and linear velocity are related through the radius of rotation. Angular velocity is equal to linear velocity divided by the radius of rotation.

3. What factors affect the angular velocity of a particle rod system after impact?

The angular velocity of a particle rod system after impact is affected by the mass, shape, and velocity of the particles, as well as the properties of the rod such as its length and material.

4. How is the angular velocity of a particle rod system calculated?

The angular velocity of a particle rod system after impact can be calculated using the principle of conservation of angular momentum. This involves calculating the moment of inertia of the system and using it in the equation: angular velocity = angular momentum / moment of inertia.

5. What are some real-world applications of studying the angular velocity of particle rod systems?

Studying the angular velocity of particle rod systems can have applications in fields such as physics, engineering, and biomechanics. It can be used to understand the motion and behavior of rotating objects, as well as to design and improve various mechanical systems and structures.

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