Physics
posted by Mann .
A 1.6 kg mass and a 6 kg mass are connected by a massless string over a pulley that is in the shape of a solid wheel having a radius 0.13 m and mass 5.5 kg. Determine the linear acceleration of the blocks.

m₁a= m₁g+T₁ …….(1)
 m₂a=T₂ m₂g ……(2)
Iε=(T₂T₁)R => T₂T₁ = Iε/R=Ia/R²
If the wheel is disc I=mR²/2 =>
T₂T₁= Iε/R= mR²a/2R²=ma/2
subtract (2) from (1)
m₁a+ m₂a=  m₁g +T₁ T₂+m₂g.
a(m₁+ m₂) = g(m₂m₁)  (T₂T₁)=
= g(m₂m₁)  ma/2.
a(m₁+ m₂+m/2)= g(m₂m₁)
a= g(m₂m₁)/(m₁+ m₂+m/2)
(If the wheel is the hoop I=mR² =>
T₂T₁= Iε/R= mR²a/R²=ma)