Calculating Angular Velocity and Time for Insect on Rotating Rod

[Shahid0072]

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..

 

[Shahid0072]

Tim..Torque is variable..We know change in angular momentum ..What can we do?

 

[tiny-tim]

Tim..Torque is variable..We know change in angular momentum ..What can we do?

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.

 

[Shahid0072]

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?

 

[tiny-tim]

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?

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.

 

[Shahid0072]

Oh..Pardon..Its 7MLL/48 Instead of 7MLL/12..Sorry..But what can we do to calculate V?

 

[tiny-tim]

Oh..Pardon..Its 7MLL/48

That's better!

ok, then, as you said …

¥(angular velocity)=12V/7L

Now use τ = 12V/7L dI/dt.

 

[Shahid0072]

But torque is variable??

 

[Shahid0072]

Its a function of both x and § as stated earlier..How can we find V in numerals by using that!