Solid cylinder: H=0.14m, R=0.05m. Mass density ∂=900-(900r/0.05), where r is distance from axis of the cylinder.
A string of negligible mass and length 0.85m is wound around the cylinder, which is set spinning by a horizontal pull on the string with F=2.5N. The cylinder starts from rest and the string is pulled off. Assume no friction between the cylinder and surface on which it rests.
a) Compute the mass, and moment of inertia around its axis, of the cylinder.
b) What is the final velocity and angular velocity of and about the CoM of the top?
c) Compute the final KE of the cylinder. Show this corresponds to work done by force F.
The Attempt at a Solution
a) Not sure at all about either of these, they look wrong to me but not sure what to do...
dm = 0.5*R2*h dθ *∫∂dr =0.1575
M = [2π,0]∫0.1575 dθ = 0.99kg
I = 0.5*M*R2 = 1.24*10-3
τ = Fl=2.5N*0.05m = 0.125Nm
α = τ/I = 101rad.s-2
ω = αt
Don't know where to go from here...