A ring as shown in the 'figure' is made up of two semi circular rings A and B of masses " 2 Kg " and " 4 Kg " respectively. The ring has diameter " 1 m ". If the Ring rolls without slipping, Find -
1. " Angular Acceleration "
2. " Normal Reaction " and
3. " Frictional Force "
30Clearly, normal reaction here N = Mgcosθ where M=6kg
Now,
since pure rolling takes place,
v=ωr or a=αr
Mgsinθ - f = Ma [f is force of friction] ... (i)
\tau = I\alpha ... (ii)
where I = m1R2 +m2R2 [ m1+m2 = 6]
since torque applied is by force of friction,
f=Ia/r2 ... (iii)
Put (iii) in (i),
a=mgsinθ/(m+I/r2)
α=a/r
and f = Ia/r2
71I don't think it's coming. However I may be wrong in Putting " I " Values.
The original answers are -
α = 6.7 rad/s2
N = 46.656 N
f = 9.302 N