Hav a conceptual rotational doubt.....(ill try nd attach the diagram)...this is related to the rotational problem asked in if im not mistaken 1994...... a cylinder of mass 'm' and radius 'R' kept on the edge of a table.......given a slight impulse...find the angle at which the cylinder looses contact with the table.....the soln in books goes this way.......let @ be angle with vertical.......conserving energy.................. MgR(1-cos$)=1/2mv2.........then. we have at pt of contact loss........mv2/R= Mgcos$......solving the two eqns. we have cos$=2/3........but why cant i go ahead and do the same thing as MgR(1-cos$)=1/2Iw2 where I=3/2MR2.....and have at the pt of contact loss as Mw2R=Mgcos$...........but using this i get cos$=4/7.......definitely i have gone wrong some where........i use the fact that loss in potential energy=gain in rotational kinetic energy about pt of contact........plz pt out where im messing it up........i know ths is too late for me to know it but i have a love for ths subject and would love to know the mistake........rates assured.....

i think that ur val of I is wrong. as the cylinder has thickness as well as length (sat L), I should be = mR2/4 + ML2/3. the formula for the moment of inertia about an axis perpendicular to the lenght of the cylinder and passing though the mid point of the lengh of a cylinder of radius R = mR2/4 + mL2/12.



when R is very small we neglect the first val to get mL2/12.

boss paranthu im interested in calculating the moment of inertia of the cylinder about an axis parallel to the central axis of the cylinder and passing through the curved surface of the cylinder.......ok for simplicity concider a disc instead of a cylinder......in the case of a disc i will to calculate the MI abt an axis parallel to the central axis and passing thru' at pt on the circumference of the disc......=MR2/2 +MR2=3/2MR2....

but still im somewhere messing it up .....some one plz pt out the mistake.....the experts plz.....

@ pramod6990 ur method is perfectly correct the book ans is wrong

see acording to the book method

but there will also be rotational KE which they have neglected it. the correct eq is

one more method is what u have done when u consider about the point ov contact then onle pure rolling

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yaar sorry im not able to attach a diagram.......but ill give u a side look of the problem......imagine the face to be the side view of the cylinder(the circular face).....and the cylinder is kept right at the corner of the table......ive tried my level best to give a picture of the problem with limited resouces.....

thnks every body...... i never knew that the books hav given a wrong soln. to this problem....seeing the soln. in the book mere funde ke faluda ban rahe the....thnks a lot....to KrishnaGopal sir and RyuAmkusa...along with Raghudevan and saideepsudi.....thnks again evrybody.....