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anonymous

  • 5 years ago

in circular motion angular mometum is cont. or angular velocity is constant??

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  1. JamesJ
    • 5 years ago
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    In uniform circular motion, is angular momentum a constant, is that what you're asking? The answer is it depends. Angular momentum, L, is by definition \[ L = r \times p = r \times mv \] This will be constant if you're measuring angular momentum from the center of the circle of motion. But for all other points, it is not.

  2. anonymous
    • 5 years ago
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    and angular velocity differ at every point rit

  3. JamesJ
    • 5 years ago
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    correct, because the vector r changes with the point from which you're measuring it.

  4. anonymous
    • 5 years ago
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    i m tired to xplain this thing to arvind he is not listening.. and even accepting !!! well thnx for help he believes u thats y i ask u too ans..

  5. AravindG
    • 5 years ago
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    but if r is same ??

  6. anonymous
    • 5 years ago
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    now u agree arvind

  7. AravindG
    • 5 years ago
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    is angular velocity same?

  8. anonymous
    • 5 years ago
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    but do u know its linear velocity??

  9. JamesJ
    • 5 years ago
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    To be explicit, suppose a body of mass m = 1 kg is moving in uniform circular motion in the xy-plane about the origin at a distance R at an angular velocity \( \omega \). Then the displacement vector r(t) is given by \[ r(t) = R(\cos \omega t, \sin \omega t, 0) \] The velocity is given by differentiating, \[ v(t) = R \omega (- \sin \omega t, \cos \omega t, 0) \] The angular velocity of as measured from the origin is \[ L = r \times mv = r \times v \] \[ = R^2\omega (0, 0, \cos^2 \omega t + \sin^2 \omega t) \] \[ = R^2\omega (0,0,1) \] This is constant.

  10. AravindG
    • 5 years ago
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    so angular velocity is constant??

  11. anonymous
    • 5 years ago
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    yea by thi it is concluding linear velocity is const. means angular velocity is const. if r is same

  12. JamesJ
    • 5 years ago
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    Provided the motion is uniform (i.e., constant angular velocity omega) _and_ we are measuring angular velocity from the origin, the center of the motion. As an exercise, calculate L if we measure r from an arbitrary point (a,b). You will see it is not a constant.

  13. anonymous
    • 5 years ago
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    wat abu my sentence i wrote i become confuse

  14. JamesJ
    • 5 years ago
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    Or even an arbitrary point (a,b,c) where this is not = (0,0,0)

  15. anonymous
    • 5 years ago
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    by ur exmple

  16. JamesJ
    • 5 years ago
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    In uniform circular motion, UCM, the vector r is not a constant, nor is the vector v. What is constant is the angular speed \( \omega \).

  17. AravindG
    • 5 years ago
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    oh cnfusing

  18. anonymous
    • 5 years ago
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    ok... got it got it thnx i think brent need ur help luk at his

  19. JamesJ
    • 5 years ago
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    The _magnitude_ of r and v are constant. But the vectors themselves are not constant, as written above.

  20. JamesJ
    • 5 years ago
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    The magnitude of r, \( |r| = R \), a constant. The magnitude of v, \( |v| = R\omega \), is also a constant.

  21. AravindG
    • 5 years ago
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    and w is const for UCM??

  22. JamesJ
    • 5 years ago
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    Yes, by definition.

  23. anonymous
    • 5 years ago
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    i dont have any more medals so that i can give u :(

  24. JamesJ
    • 5 years ago
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    If \( \omega \) was not constant, then the object would not be moving around at the same rate for all \( t\). But we define UCM to to be the angular velocity \( \omega \) is constant.

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