What Is the Velocity of the Center of Mass of the Disk?

[ohheytai]

What is the speed of the center of mass of the disk?
A string is wrapped around a disk of mass m = 1.5 kg and radius R = 0.11 m. Starting from rest, you pull the string with a constant force F = 6 N along a nearly frictionless surface. At the instant when the center of the disk has moved a distance x = 0.10 m, a length d = 0.31 m of string has unwound off the disk.

(a) At this instant, what is the speed of the center of mass of the disk?

(b) At this instant, how much rotational kinetic energy does the disk have relative to its center of mass?

i know Krot is 1/2(I\omega^2
but i have no clue how to do the first part
i know Vcm is Mass*v + mass*v2 +... over Total mass but yaa i don't know how to do this someone help!

 

[zalnas]

I've got the same assignment due tonight.

For the first part, you can set Kinetic Energy equal to the work done on the disk, W=Fd. d is the distance the center of the disk moves. From there, just solve for v, so:

Fd = .5*m*v²

Were you able to get the second one?

 

[Cattzs]

For the second question, it's like the PRS example in class.
You have to analyze the system first as a point particle system, then as a real system.

SO:
PP-
delta E sys = W surr, pp
delta K trans = W surr = F (dot) delta r CM
delta K trans = Fx

Real -
delta E sys = W surr, real
delta K trans + delta K rot = F (x + d)
delta K rot = F(x + d) - Fx
since K rot, i = 0
K rot, f = Fd

 

[zalnas]

I tried

K_rot,f = F*d

where d is the distance the center of mass moves, but I got the incorrect answer, and it was my last try. Oh well, I must've used a wrong number. Thanks for your help though!

 

[Cattzs]

I tried

K_rot,f = F*d

where d is the distance the center of mass moves, but I got the incorrect answer, and it was my last try. Oh well, I must've used a wrong number. Thanks for your help though!

d was actually supposed to be the length that the string unwound.
These questions are quite confusing. lol

 

[zalnas]

Damn. That makes sense now that I think about.

 

[Cattzs]

Damn. That makes sense now that I think about.

Yeah. lol
At least you see how to do it now?

 

[zalnas]

Yes I do. Thanks for your help.