Conservation of momentum and a uniform rod

In summary, a uniform rod with a length of 0.60 m and a mass of 1.0 kg rotates in the plane of a figure about an axis through one end, with a rotational inertia of 0.12 kg·m2. When it collides with a 0.20 kg putty wad at its lowest position, the resulting angular speed of the rod-putty system is 1.5 rad/s.
  • #1
mmiller9913
14
0

Homework Statement



The uniform rod (length 0.60 m, mass 1.0 kg) in Fig. 11-54 rotates in the plane of the figure about an axis through one end, with a rotational inertia of 0.12 kg·m2. As the rod swings through its lowest position, it collides with a 0.20 kg putty wad that sticks to the end of the rod. If the rod's angular speed just before collision is 2.4 rad/s, what is the angular speed of the rod–putty system immediately after collision?

http://edugen.wiley.com/edugen/courses/crs4957/halliday9118/halliday9118c11/image_n/nt0058-y.gif

Homework Equations


IW=IW

I=mr^2

The Attempt at a Solution



IW=IW
.12(2.4) = (.12 + mr^2) Wf
.12(2.4) = (.12 + .20(.60)Wf
Wf= 1.2 rad/s

Homework Statement


Homework Equations


The Attempt at a Solution


Homework Statement


Homework Equations


The Attempt at a Solution

 
Last edited:
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  • #2
i know .12 = 1/3ML^2
 
  • #3
.12 is in the problem because its the inertia of the rod both before and after the collision
 
  • #4
Sorry, it's been a while since I've done one of these problems.

Everything is correct, you just forgot to square the radius on the right hand side.

.12(2.4) = (.12 + .20(.60)Wf should be .12(2.4) = (.12 + .20(.60)^2)Wf

Wf is then 1.5 rad/s.
 
  • #5
o wow forgot to square r, heh sorry
 

1. What is conservation of momentum?

Conservation of momentum is a fundamental law of physics that states that the total momentum of a closed system remains constant over time. This means that the total amount of momentum before and after an interaction or event must be the same.

2. How does conservation of momentum apply to a uniform rod?

A uniform rod is an example of a closed system, meaning there are no external forces acting on it. As such, the total momentum of the rod must remain constant. This means that if one end of the rod experiences a force, the other end will experience an equal and opposite force to maintain the total momentum of the system.

3. What factors affect the conservation of momentum in a uniform rod?

The conservation of momentum in a uniform rod is affected by the mass, velocity, and direction of the rod. Any changes in these factors will result in a corresponding change in the momentum of the rod.

4. Can conservation of momentum be violated?

No, conservation of momentum is a fundamental law of physics and cannot be violated. In a closed system, the total momentum must remain constant, even if individual object's momentum changes.

5. How is conservation of momentum related to other laws of physics?

Conservation of momentum is closely related to Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction. The conservation of momentum also has applications in other areas of physics, such as collisions, explosions, and projectile motion.

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