accha.....heres a nice problem in rotational mechanix.........ill say only those attempt this one who havnt seen this problem before..........ok there's a Disc of mass 'M' and radius 'R'......it is rolling abt a horizontal axis passing thru the centre(bole to rlling on the ground yaar).......with a velociyt of its centre of mass as ' v₀'...........its pure rolling.................as it pure rolls it comes accross an inclined plane of inclination'  '............find the lenght it covers on the inclined plane that it covers before coming to rest..........again i say only those try it who havnt seen this one before........

is there no one that can attempt this one?????

cmon' guyz......im sure u all can do this one........come ahead and give a try.............

i think its      3 v^2 / 4g.

am i correct

i have given the vertical height and not the distance ( lenght ) covered on the plane.

the length covered on the plane =  3 v^2 / 4gsin@ .

No dude........uve made the common mistake that many make........hav u conserved energy.......well if u have ....u are wrong............

question is very easy .so if any error exist it is due to calculation else i m a 100% error free man

mgsin@-f=ma

fr=IA

a=RA

mgsin@-iA/R=ma

mgsin@-iA/R^2=ma

a=mgsin@/(m+i/r^2)

a=2gsin@/3

s=3V^2/4gsin@

if there is an error then tell me........always ready to help others

Blade X this Q. is not as nice and sweet as i seems to u....if it was just abt writing the force eqn. and torque eqn. and solving for the final distance covered before coming to rest.....i wudnt have wasted my time posting this problem.......ill point out ur error.....u assume that as soon as the disc starts to climb up the incline plane its velocity is same as V₀ and its angular velocity is  V₀/R............this very fact is wrong......so u err evn before u begin the first step of ur soln.......this is a big hint that im giving u........

OK....so im giving a hint at this stage....before climbing up the plane......it colides with the plane........now if this collision were to be perfectly elastic......the disc wudnt be climbing up the plane...infact it wud be rebounding away frm the inclined plane..........so folks the collision is not elastic.......and thus ur energy conservation techiniques or assumption of same velocity after climbing up the plane doesnot work here..........

wats happening here is clearly enelastic............infact completely inelastic...........before collision it had some component of velocity along the line of impact after collision it is travelling along the incline plane implying that it has no velocity parallel to the line of impact yaar...........