# Cylinder pulled by string on flat surface w/out slipping

1. The problem statement: a 100kg homogeneous cylinder of radius .3m. Starts at rest. Is pulled by a string wrapped around the cylinder coming off the top with a force of 500N.

Find the angular velocity after the cylinder has rolled one revolution?

The attempt at a solution: I= 4.5kg*m^2

circumferance=1.885m

work= 500*1.885= .5m(wr)^2+.5Iw^2 (using w for omega)

can someone please explain. I suppose the force could be doing rotational work as well but I'm having a hard time believing that the force does double the work because of where it is applyed.

My question is which answer is correct and WHY? thanks for any help

tiny-tim
Homework Helper
Welcome to PF!

Hi highroller! Welcome to PF! (have an omega: ω and try using the X2 tag just above the Reply box )
a 100kg homogeneous cylinder of radius .3m. Starts at rest. Is pulled by a string wrapped around the cylinder coming off the top with a force of 500N.

Find the angular velocity after the cylinder has rolled one revolution?

work= 500*1.885= .5m(wr)^2+.5Iw^2 (using w for omega)

Yes intial energy is zero, so work done = final energy. But what is your .5m(ωr)2 supposed to be?

There's no extra mass … it's only a cylinder, with energy 1/2 Iω2 the cylinder has both linear and rotational ke so the .5m(wr)^2 comes from .5mv^2 with v=wr

tiny-tim
ah, sorry … i looked at your 500*1.885 and assumed that the axle was fixed. Hint: how fast is the string moving? 