- #31
Shahid0072
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Tiny tim...Which equations?
Calculating Angular Velocity and Time for Insect on Rotating Rod
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The discussion revolves around calculating the velocity (V) of an insect that lands on a rotating rod and determining the time it takes for the insect to move from the midpoint to the end of the rod while maintaining a constant angular velocity. Participants emphasize the importance of conservation of angular momentum, noting that while the angular momentum changes, the angular velocity can remain constant due to the balance of torques acting on the system. The moment of inertia increases as the insect moves away from the pivot, which tends to slow the rod's rotation, while the torque from the insect's weight can increase the angular speed. The key challenge is to derive the equations necessary to calculate V and the time taken for the insect's movement, with suggestions to express torque and moment of inertia as functions of the insect's position. Overall, the problem requires careful application of physics principles to find the numerical values for V and the time taken.
- #32
tiny-tim
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Do you mean you can't read the symbols below?
(if you can, just copy one and paste it
)
(if you can, just copy one and paste it
)- #33
Doc Al
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Moderator's note: Moving to Intro Physics, since this is more about solving a particular problem than about broader conceptual issues.
- #34
Shahid0072
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M writing thru my cell..Its not allowing me to click on those letters..I can just c them
- #35
tiny-tim
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Shahid0072 said:
The equation which relates the speed V to the angular velocity ω,
and the τ = ωdI/dt equation
(with all the numbers, please
).- #36
Shahid0072
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I wrote it..We are just given Length of rod (L)in numbers which is 1.8 m..And i wrote already that ¥(angular velocity)=12V/7L..We have to calculate V in nos..
- #37
Shahid0072
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Tim..Torque is variable..We know change in angular momentum ..What can we do?
- #38
tiny-tim
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Shahid0072 said:
Call the position of the insect x, and the angle θ, and find the moment of inertia as a function of x, and the torque as a function of x and θ.
- #39
Shahid0072
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I guess u haven't read my earliear post..Torque varies as Mgx cos§ where x is insect's distance from centre and § is angle rotated by rod..Initial moment of inertia of rod +insect is 7MLL/12 AND when rod is vertical is MLL/3..How to calculate V in numbers?
- #40
tiny-tim
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Shahid0072 said:
hmm … that can't be right … 1/3 < 7/12, but the moment of inertia should be increasing.
If L is the length AB of the whole rod, then I for the rod is 1/12 ML2, to which you have to add I for the insect for L/4 ≤ x ≤ L/2.
- #41
Shahid0072
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Oh..Pardon..Its 7MLL/48 Instead of 7MLL/12..Sorry..But what can we do to calculate V?
- #42
tiny-tim
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Shahid0072 said:
That's better!
ok, then, as you said …
Now use τ = 12V/7L dI/dt.
- #43
Shahid0072
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But torque is variable??
- #44
Shahid0072
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Its a function of both x and § as stated earlier..How can we find V in numerals by using that!