1Any one? Is it too tough to be answered?
23(not sure )
let the upper ring be denoted by 1 and lower by 2
we have :
m1v1 = m2v2...............(1)
( v1 & v2 are vel of respective com )
by energy conservation ,
m2gr2= KE due to pure translation of com of the rings + KE due to pure rotation of rings abt their com
= 12m1v12 + 12m2v22 + 12I1ω12 + 12I2ω22 .............(2)
now for the topmost pt of the upper ring ,
v = 0 = r1ω1 - v1
so v1 = r1w1....................(3)
consider the pt common to both rings
v = v1 + r1ω1 = 2v1 = r2ω2 - v2 ......(4)
4 eqns , and v1,v2, ω1,ω2 are the 4 unknowns , it shud get solved ...
1
swordfish
·2011-01-24 11:12:17
Thanks for reply qwerty. I solved the question anyways.
You made it too complex :p.....there is no need to consider the rotation of the smaller ring as it does not rotate until the bigger ring passes the vertical position... and we are required to find angular velocity of the bigger ring just at the vertical position....so no rotation of the smaller ring [1]
23
qwerty
·2011-01-24 23:55:24
"as it does not rotate until the bigger ring passes the vertical position"\
are you sure ?
71v = 0 = r1ω1 - v1
so v1 = r1w1....................(3)
consider the pt common to both rings
v = v1 + r1ω1 = 2v1 = r2ω2 - v2 ......(4)
I can't get this!
1
swordfish
·2011-01-25 13:11:36
@qwerty:
No I don't have any theoretical explanation for that........I performed it by taking two such rings ( I have one such setup at home [3] ). I found that the upper ring does not rotate (only translates) till the bigger ring reaches the vertical position. After that, it rotates (though by only a very small angular velocity)
1@swordfish
buddy tell me one thing don't u think we will need the radius of small ring??...else there will be three equations in four unknowns[after all r=radius of small ring is also an unknown] as i am getting right now.....something is missing out here in the problem[12]
23
qwerty
·2011-01-25 20:13:05
oh!!!!!!! i made an error there , i though that upper ring's upper end is fixed ..... ok ok , then we wont have ω1
so we will have
m1v1 = m2v2
m2gr2 = 12m1v12 + 12m1v12 +12I2ω22
v1 = r2ω2 - v2
& assuming the rings to be uniform and of equal density , r1/r2=m1/m2
