- #1
Dusty912
- 149
- 1
Homework Statement
I attached the stated questions. Mainly need help with question 2. See below for my answer to question 1.
Homework Equations
ΣT=Iα
ΣF=ma
moment of inertia of sphere: I=(2mR^2)/5
moment of inertia of disk: I=(mr^2)/2
v=rω
V(center of mas)=V(tangential) -because of smooth rolling
ΔΘ=ωt+(1/2)αt^2
ω(final)=ω(initial)+αt
ω^2(final)=ω^2(initial) +2αΔΘ
The Attempt at a Solution
1. C) 4F1 -I figure the lever arm is 1/4 as big for the smaller disk so it would require a force 4 times as big to counteract the force applied to the larger disk.
2. a) I know how to draw the FBD for this.
B) what I need the most help with. It has been a while since we have done this section and I had trouble with it the first time. But I am assuming we use the analogy for Newton's second law ΣT=Iα and the sum the torques. But do I do this for the sphere and the the disk together? not really sure. My guess is that it would look something like this. T1=the tension in the rope tangential to the sphere and disk.
T2=the tension in the rope tangential to the disk and connected to the block.
So summing the torques for the sphere: T1R=(2/5)mR^2α -the radius would be of the sphere of course
Summing of the torques for the disk: T2r=(1/2)mr^2α
and summing of the forces for the block would be T2-mg=ma (the m's would be the mass of the block)
from here I'm stuck. Sorry I couldn't show more work but like I said I really need help with this one.
Part (c) should be pretty easy once I know the acceleration of the black from part B