- Homework Statement:
A plane, homogeneous disk may slide on a frictionless horizontal table. A
light cord is fastened to the disk and wrapped many times around the rim of
the disk. The cord goes without friction through a small eyelet at the edge
of the table and is connected to a mass m (see the figure). The mass of the
disk is M and its radius is R. The system is started from rest and the cord
is assumed to be taut throughout the motion. Ignore the mass of the cord.
(1) Find the velocity v of the center of mass of the disk as a function of time
(before the disk hits the eyelet or the mass m hits the floor).
- Relevant Equations:
- N = dL/dt
mgR = d(mvR + MvR + ½M(R^2)v/R)/dt
mgR = ma + Ma + ½Ma
mg = a(m + 3/2M)
v = mgt / (m+3/2M)
My answer is incorrect. The right answer is v = mgt/(3m+M), but I have no idea what I'm doing wrong.