M3 Circular Motion Help

Bengaltiger

OB is a light rod of length 5l. Particles of masses 3m and 4m are attached at points A and B of the rod, where OA is 2l. The rod is made to rotate about O in a horizontal plane with constant angular speed W. Calculate the ratio of the tensions in OA and AB.

Thanks in advance.

T_A = m_Aw²r_A
T_B = m_Bw²r_B

T_A = 3m x w² x 2l
T_B = 4m x w² x 5l
T_A / T_B = 3/10

Reply 2

OP

Hmm...that was my initial anwser. Book has 13:10 as ratio...

Reply 3

i think that the 1 in the 13 is a typo...

Reply 4

OP

probably....thnx

Reply 5

ok.. i thought about it again: it is 13/10...

T_OA = 3m x w² x 2l + 4m x w² x 5l = 26 mw²l
T_AB = 4m x w² x 5l = 20mw²l
T_A / T_B = 13/10

Reply 6

OP

In tension OA, why are you adding the tension in AB aswell?

Reply 7

well ok:
the rod is pulling the mass at B with tension 20mw²l, i.e. any part of the rod from O to B is pulling the mass at B with that tension...
also: the rod is pulling the masss at A with tension 6mw²l, i.e. any part of the rod between O and A is pulling the mass at A with that tension.

so the tension on the part AB is 20mw²l.
but the part OA has both the tension to pull A and to pull B... i.e. 20mw²l + 6mw²l.
got it?

Reply 8