- #1
cosurfr
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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!
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?
*Lf=angular momentum final
*Lo=angular momentum initial
Conservation of angular momentum: L=Iw -> Lf=Lo -> Iwf=Iwo, wo=0
Iwf=0
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
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