Momentum Conservation: Ball Hitting Pivoted Rod

In summary, the conservation of both linear and angular momentum depends on whether the system is closed or not. If the other end of the pivot is attached to the Earth, the rod+ball system is not closed and the forces applied by the pivot can change both the linear and angular momentum. However, in this particular case, where all the forces pass through the hinge and the hinge is used as the axis for calculating angular momentum, angular momentum is conserved. According to Klepner's introduction to mechanics, only linear momentum is not conserved.
  • #1
Zubair Ahmad
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If a ball hits a rod at the top which is pivoted at bottom end then is linear momentum conserved?
 
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  • #2
Zubair Ahmad said:
If a ball hits a rod at the top which is pivoted at bottom end then is linear momentum conserved?
Both linear and angular momentum are conserved as long as the system is closed (that is, you're considering total for the the ball, the rod, and whatever the other end of the pivot is attached to). If the other end of the pivot is fastened directly or indirectly to the Earth and you are treating the Earth as completely immobile (which is a really good simplifying assumption here) then rod+ball system is not closed, and the forces applied by the pivot to the rod can change both the linear and the angular momentum of that system.
 
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Likes Dale
  • #3
But as written in Klepner introduction to mechanics only linear momentum is not conserved.
 
  • #4
In this particular case, all the forces @Nugatory is talking about pass through the hinge, so are always radial and don't affect angular momentum about the hinge. So angular momentum is conserved, yes. That isn't generally true, but it is in this case.
 
  • #5
Ibix said:
pass through the hinge, so are always radial and don't affect angular momentum about the hinge
If you are using the hinge as the axis about which angular momentum is calculated than no force at the hinge (radial or otherwise) can ever affect angular momentum. The moment arm is zero. The force at the hinge is not limited to being in the radial direction. The hinge can and will produce a shear force just as easily. Hence wheelbarrows.
 
  • #6
Zubair Ahmad said:
But as written in Klepner introduction to mechanics only linear momentum is not conserved.
I said "can change", not "will change". Whether this interaction will conserve angular momentum or not depends on what assumptions you make about the detailed behavior of the pivot; a textbook like K&K will typically assume an idealized pivot and in that case angular momentum will be conserved.
 

What is momentum conservation?

Momentum conservation is a fundamental principle in physics that states that the total momentum of a closed system remains constant. This means that the initial momentum of an object will be equal to the final momentum of the same object after a collision or interaction.

How does momentum conservation apply to a ball hitting a pivoted rod?

In the case of a ball hitting a pivoted rod, the total momentum of the system (ball and rod) before and after the collision will remain constant. This means that the initial momentum of the ball will be equal to the final momentum of the ball and rod combined.

What factors affect momentum conservation in a ball hitting a pivoted rod?

The factors that affect momentum conservation in this scenario include the mass and velocity of the ball, the length and mass distribution of the pivoted rod, and the angle at which the ball hits the rod. These factors can impact the final momentum of the system after the collision.

How is momentum conserved in a perfectly elastic collision between a ball and a pivoted rod?

In a perfectly elastic collision, both kinetic energy and momentum are conserved. This means that the total momentum of the system before and after the collision will remain constant, and the kinetic energy of the system will also remain the same.

What happens to momentum in an inelastic collision between a ball and a pivoted rod?

In an inelastic collision, kinetic energy is not conserved, but momentum is still conserved. This means that the total momentum of the system will remain constant, but some of the kinetic energy will be converted into other forms of energy, such as heat or sound. The final momentum of the system after the collision will be less than the initial momentum of the ball.

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