Rotation and Linear Motion Help


by choi626
Tags: linear, motion, rotation
choi626
choi626 is offline
#1
Mar4-07, 11:07 PM
P: 8
1. The problem statement, all variables and given/known data

Two masses, m1 and m2, are connected by light cables to the perimeters of two cylinders of radii, r1 and r2, respectively. The cylinders are rigidly connected to each other but are free to rotate without friction on a common axle. The moment of inertia of the pair of cylinders is I = 45 kgm^2.
r1= 0.5m
r2= 1.5m
m1= 20kg
a) Find the mass of m2 so that the system is in equilibrium
b) the mass is removed and the system released from rest. Determine the angular acceleration, the cable supporting m1, and the linear speed of m1 at the time it has descended 1m.

3. The attempt at a solution
a) T=0
r1F1 - r2F2 = 0
m2= 6.7kg.

b)T=I(alpha)
then how do i go on?
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denverdoc
denverdoc is offline
#2
Mar4-07, 11:34 PM
P: 1,351
What do you visualize happening to the mass and cylinders after the balancing mass is removed?
choi626
choi626 is offline
#3
Mar5-07, 12:13 AM
P: 8
the wheel rotating in the direction of the heavier mass.

okay umm so my teacher wrote that i have to connect the bodies as well. do i combine the inertias of the two masses

I = I(of m1) + I(of m2).

originally i had (0.5)(20)(9.8)=45(alpha)

but he marked it wrong saying i need to connect the bodies. I dont think i fully understand what he means.

denverdoc
denverdoc is offline
#4
Mar5-07, 12:48 AM
P: 1,351

Rotation and Linear Motion Help


w/o a pic, not sure either. I was under the impression that the cylinders were held stationary while the balancing mass was removed and then allowed to accelerate. In other words you had one mass, two cylinders and a brake which was released at t=0
choi626
choi626 is offline
#5
Mar5-07, 12:57 AM
P: 8
yea so i was kinda pissed he didnt put a pic on the test too. but he said that the cylinders are instantaneously stationary when the mass is removed. The smaller cylinder he said can be considered to be inside the big one. The only reason for the two radii is for the inertia equations for the masses.

thanx for replying
denverdoc
denverdoc is offline
#6
Mar5-07, 01:04 AM
P: 1,351
ok, then the reason they are "connected" is thru the need to conserve momentum. I'm headed for zzzzland, suspect there will be more on this issue in the morning.


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