Question

A rope is wrapped around the curved side of a cylinder .600 m in radius. A mass of 10.0 kg is suspended from the free end of the rope. If the cylinder is free to rotate about its long axis as the rope unwinds, what is the angular acceleration of the cylinder if its moment of inertia is 5.00 kgm2? Ignore the mass of the rope.

Answer 1

If the cord does not slip

M=R*T=I*α ⇒T = I·α/R

T-m*g=-m*a ⇒ T=m*g-m*a

α=a/R

So ,

m*g-m*a = I*α/R = I*a/R²

⇒ I*a/R² + m*a= m*g

⇒ a=g/{1 + I/(m·R²)}

⇒ α=g/{R + I/(m·R)}

Where

M=Cilinder mass

I= Moment of inertia

a=acceleration

α=angular acceleration

m=mass suspended

R=radius

g=gravity

Considering g=9,81 m/sec²

α=10,75 {rad/sec²}