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.

Answer 1

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

(If the wheel is the hoop I=mR² =>
T₂-T₁= Iε/R= mR²a/R²=ma)