Rotation - Collision of Rotating Cylinders Cylinders

In summary, the book says that you can solve an equation for the angular momentum of two objects if you know their moments of inertia about their centers of mass. However, the book says that this method is wrong because the torque about the center of mass is zero.
  • #1
cupid.callin
1,132
1

Homework Statement



attachment.php?attachmentid=33231&stc=1&d=1300475161.jpg



The Attempt at a Solution


The book did it like taking impulse of forces f and writing eqn Impulse = Δ(Angular momentum)
or J = ΔL

How i tried:

attachment.php?attachmentid=33232&stc=1&d=1300475161.png


let the 2 cylinders meet at A

(they have not mentioned the velocity of approach but as it says that the 2 cylinders remain in contact and don't fly off after collision so i guessed that velocity is negligible)

Considering Torque at A
As no torque acts during whole process so L about A remains constant

[tex]L_{initial} = I_1w_1 \ - \ I_2w_2[/tex]

now let that after they meet and friction does it work they have angular speeds w1' and w2'

[tex]L_{final} = I_1w_1' - I_2w_2'[/tex]

and also

[tex]w_1'r_1 = w_2'r_2[/tex]
as the point of contact of 2 cylinders has same velocity

But this gives wrong answer!

Can someone tell me why this method is wrong?
 

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  • #2
hi cupid.callin! :smile:

your method should work :confused:

can i check … when you said …
cupid.callin said:
As no torque acts during whole process so L about A remains constant

… did you calculate L using the moments of inertia about the centres (which is correct), or about A (which isn't) ?
 
  • #3
tiny-tim said:
… did you calculate L using the moments of inertia about the centres (which is correct), or about A (which isn't) ?

moment if inertia of a body about any point,

[tex] \vec{L} = \vec{L}_{CM} + m\vec{r}X\vec{v}_o[/tex]

where vo is velocity of CM

And as i said that cylinders do not fly away after collision, vo ≈ 0

So

[tex] \vec{L} = \vec{L}_{CM}[/tex]
 
  • #4
And if the torque about A is zero then shouldn't momentum be conserved about A and thus calculate moments of inertia about A ?

If i calculate moments of inertia along CM then the friction will have torque and then momentum is not conserved !
 
  • #5
hi cupid.callin! :smile:
cupid.callin said:
[tex] \vec{L} = \vec{L}_{CM}[/tex]

yes, that's right …

LA = Lc.o.m.

but you said you used the formula Iω for LA, so i was just checking whether you used IAω or Ic.o.m.ω :wink:
 
  • #6
What form is the answer in?

Can you show your solution?
 

1. What is rotation and how does it relate to the collision of rotating cylinders?

Rotation is the movement of an object around a fixed point or axis. In the case of the collision of rotating cylinders, it refers to the spinning motion of the cylinders as they come into contact with each other.

2. How do the velocities of the cylinders affect the collision?

The velocities of the cylinders play a crucial role in the collision. If the velocities are similar, the cylinders will collide with each other and continue to rotate together. If the velocities are different, the cylinder with the higher velocity will transfer some of its energy to the other cylinder, causing it to speed up and rotate in the same direction.

3. What is the conservation of angular momentum and how does it apply to this collision?

The conservation of angular momentum states that the total angular momentum of a system remains constant unless acted upon by an external torque. In the case of the collision of rotating cylinders, the total angular momentum before and after the collision will be the same, as long as there are no external torques acting on the system.

4. How does the mass and size of the cylinders affect the collision?

The mass and size of the cylinders have a direct impact on the collision. The larger and heavier the cylinders, the more force will be exerted on each other upon collision. This can lead to a more significant transfer of energy and a change in the direction of rotation.

5. Can the collision of rotating cylinders be applied to real-world scenarios?

Yes, the collision of rotating cylinders can be observed in many real-world scenarios, such as the collision of gears or the spin of a top. It is also an essential concept in fields such as mechanical engineering and physics, where it is used to calculate the motion and energy of rotating objects.

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