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A maths teacher said I am wrong but never explained why. Confused...
Okay, thank you!
Oh yes, I'm terrible for only half reading the question. It does ask 'how fast' so I guess they want the velocity.
I've studied moments of inertia before (had to do it for my exam) and deriving them via integration -- but I know the M.I. of the rod is definitely correct (and therefore the change in KE). Since:
as v = rw. But, this question still confuses me... are they asking for the ANGULAR velocity w, or just the instantaneous velocity of the end of the rod? In which case, with r = l;
v = rw, using my w from post #1;
...... stopped thinking
I would have to look at this in the morning. My brain is not functioning properly right now.
For a uniform rod of mass m and length 2l, the moment of inertia about an axis perp. to the rod through the centre is ml2/3 (you can prove this by integration but it should be fine to quote it). For a rod of length l, you square (l/2) instead. Then apply the parallel axis theorem, to get the M.I. of the rod about the axis through the end. I sort of wasted time thinking about I_x, I_y and I_z, since it is a rod, not a lamina, and therefore I_y = I_z.
Oops! Me and my careful reading. Didn't see the "also touches the wall" part. Sorry.
I don't see how else this could be interpreted... clearly the starting position is the rod in its horizontal position.
But, the question never states the starting position of the rod.
If the rod is at first horizontal, then rotates 90 degrees (when first vertical), then the change in GPE is mgl/2, since the centre of mass of the rod has dropped by a distance of l/2.
Ok, step by step. How'd you get the loss in GPE formula?