# Disk Pulled By String

1. Apr 2, 2009

### kritzy

1. A solid uniform disk of mass 21.0 kg and radius 85.0 cm is at rest flat on a frictionless surface. A string is wrapped around the rim of the disk and a constant force of 35.0 N is applied to the string. The string does not slip on the rim.
(A) When the disk has moved a distance of 3.2 m, determine how fast it is moving.
(B) How fast it is spinning (in radians per second).
(C) How much string has unwrapped from around the rim.

2. Relevant equations
τ=RF
τ=Iα
I=.5mR$$^{2}$$
a=Rα
v$$^{2}$$=v$$^{2}_{0}$$+2ax
v=Rω

3. The attempt at a solution
(A) τ=RF=(35)(.85)=29.75
I=(.5)(21)(.85)$$^{2}$$=7.58625
α=τ/I=29.75/7.58625=3.92
a=(.85)(3.92)=3.33
v=$$\sqrt{0+(2)(3.33)(3.2)}$$=4.6
This is how I did the problem but it is incorrect.

(B)v=Rω
I want to use this formula to find the angular velocity but my velocity is incorrect.

(C)I was thinking of using this formula: θ=(ω$$^{2}$$-ω$$^{2}_{0}$$)/2α

2. Apr 3, 2009

### tiny-tim

Hi kritzy!

For (A), use the ordinary (linear) version of Newton's second law

3. Apr 3, 2009

### kritzy

I figured it out. Thank you for the hint.