Two metal disks, one with radius R_1 = 2.40cm and mass M_1 = 0.900kg and the oth

Question

Two metal disks, one with radius R_1 = 2.40cm and mass M_1 = 0.900kg and the other with radius R_2 = 5.00cm and mass M_2 = 1.50kg , are welded together and mounted on a frictionless axis through their common center. A light string is wrapped around the edge of the smaller disk and a 1.50kg block is suspended from the free end of the string.

a.What is the magnitude of the downward acceleration of the block after it is released?
Take the free fall acceleration to be 9.80;{ m m/s^{2}}.

b. Repeat the calculation of part (a), this time with the string wrapped around the edge of the larger disk.
Take the free fall acceleration to be 9.80;{ m m/s^{2}}.

Explanation / Answer

a)moment of inertia of system=0.5*0.9*0.0242+0.5*1.5*0.052=2.1342*10-3kgm2

Let T be the tension in the string.

T.r=I=Ia/r

T=3.7052a(1)

mg-T=ma   

1.5g-T=1.5a (2)

Solving for a,

a=2.824m/s2

b)

T.r=I=Ia/r (r=0.05)

T=0.85368a(1)

mg-T=ma   

1.5g-T=1.5a (2)

Solving for a,

a=6.25m/s2

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