Two metal disks, one with radius = 2.47cm and mass = 0.850kg and the other with

Question

Two metal disks, one with radius = 2.47cm and mass = 0.850kg and the other with radius = 5.00cm and mass = 1.58kg , are welded together and mounted on a frictionless axis through their common center. .

A)What is the total moment of inertia of the two disks?
B)A light string is wrapped around the edge of the smaller disk, and a 1.50-kg block, suspended from the free end of the string. If the block is released from rest at a distance of 1.98m above the floor, what is its speed just before it strikes the floor?
C)Repeat the calculation of part B, this time with the string wrapped around the edge of the larger disk.

Explanation / Answer

A) Moment inertia of a disk I=1/2 m R2

so Itotal=0.5*0.85*0.02472+0.5*1.58*0.052=0.0516

B) We'll use energy

Initially only potential energy E=mgh=1.5*1.98*9.81=29.14 J

Finally only kinetic energy E= 1/2 mv2 + 1/2 I 2

=v/r where r is where the rope is attached

E=0.5 * 1.5*v2+0.5*0.0516*v2/0.02472

Setting the two energies equal we find v=0.823 m/s

C) only difference is that the r is now 0.05 so final energy is now

E=0.5 * 1.5*v2+0.5*0.0516*v2/0.052

Setting this equal to the initial energy and solving for v, v=1.62 m/s

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