Finding angular velocity using conservation of angular momentum

In summary, the problem involves a thin rod rotating on a frictionless tabletop with an axis perpendicular to one end. The rod has an initial angular velocity of 0.32 rad/s and a moment of inertia of 1.1 x 10^-3 kg x m^2. A bug with a mass of 4.2 x 10^-3kg crawls from one end of the rod to the other. The question asks for the final angular velocity of the rod once the bug reaches its destination. The solution involves using the conservation of angular momentum equation and setting the initial angular velocity of the bug equal to the initial angular velocity of the rod. This leads to the correct answer.
  • #1
cosurfr
5
0
Hello everyone, I hope that someone can help me solve this rather than solving it for me, here's the problem and what I've done so far...oh and thanks in advance!

Homework Statement



A thin rod has a length of 0.25 m and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of 0.32 rad/s and a moment of inertia of (1.1 x 10^-3 kg x m^2). A bug standing on the axis decides to crawl out to the other end of the rod. When the bug (mass = 4.2 x 10^-3kg) gets where it’s going, what is the angular velocity of the rod?


Homework Equations


*Lf=angular momentum final
*Lo=angular momentum initial


Conservation of angular momentum: L=Iw -> Lf=Lo -> Iwf=Iwo, wo=0
Iwf=0

The Attempt at a Solution


Okay so I thought this problem seemed fairly straight forward, so hopefully I'm just doing a little algebra incorrectly or something, but here's my whirl at the answer
Iwf=0
(Moment of Inertia of rod)(ang vel of rod)+(mass of bug)(length of rod)^2(w)=0

(1.1 x 10^-3 kg x m^2)(0.32 rad/s) + (4.2 x 10^-3kg)(0.25m)^2(w)=0

(4.2 x 10^-3kg)(0.25m)^2(w)= -(1.1 x 10^-3 kg x m^2)(0.32 rad/s)

*****Now just solve for w? Or is this completely wrong? I did do the calculations but didnt want to put all that up if this wasnt even the right way to set up the problem. If someone could let me know if I'm on the right track and lend me a hint of how to proceed i'd really appreciate it. Thanks

Cosurfr
 
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  • #2
cosurfr said:
A thin rod has a length of 0.25 m and rotates ...has an angular velocity of 0.32 rad/s ...

Why did you use w0 = 0?

Go back towards the top of your proof, and use this given value for w0 instead ... see what happens.
 
  • #3
Thanks so much. Thats exactly where i went wrong. The initial ang vel of the bug would have been the same as the initial ang vel of the rod (constant). That cleared it all up. Thanks a ton for not just doing it for me but rather helping me find the way. This website is the best FYI

cosurfr
 

1. How is angular velocity defined?

Angular velocity is a measure of the rate at which an object rotates or spins around a fixed axis. It is typically represented by the symbol "ω" and its units are radians per second (rad/s).

2. What is conservation of angular momentum?

Conservation of angular momentum is a fundamental law of physics that states that the total angular momentum of a system will remain constant as long as there are no external torques acting on the system. This means that angular momentum cannot be created or destroyed, only transferred between objects in the system.

3. How can I find the angular velocity using conservation of angular momentum?

To find the angular velocity of a rotating object using conservation of angular momentum, you need to know the moment of inertia of the object, the initial angular velocity, and the moment of inertia of any other objects in the system. Using these values and applying the principle of conservation of angular momentum, you can solve for the final angular velocity of the object.

4. What are some real-life examples of conservation of angular momentum?

Conservation of angular momentum can be observed in many everyday situations, such as a spinning top, a figure skater performing a spin, or a planet orbiting around the sun. In all of these cases, the angular momentum of the system remains constant due to the absence of external torques.

5. What happens to the angular velocity if the moment of inertia changes?

If the moment of inertia of an object changes, its angular velocity will also change in order to maintain the principle of conservation of angular momentum. For example, if a figure skater brings their arms closer to their body during a spin, their moment of inertia decreases and their angular velocity will increase. Similarly, if they extend their arms, their moment of inertia increases and their angular velocity will decrease.

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