Two metal disks, one with radius R 1 = 2.37cm and mass M 1 = 0.770kg and the oth

Question

Two metal disks, one with radius R1 = 2.37cm and mass M1 = 0.770kg and the other with radius R2 = 5.03cm and mass M2 = 1.65kg , are welded together and mounted on a frictionless axis through their common center.

What is the total moment of inertia of the two disks?

Answer:

2.3010?3

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 2.04m 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.

I couldn't figure out the second two

I =

2.3010?3

  kg?m2 Two metal disks, one with radius R1 = 2.37cm and mass M1 = 0.770kg and the other with radius R2 = 5.03cm and mass M2 = 1.65kg , are welded together and mounted on a frictionless axis through their common center. What is the total moment of inertia of the two disks? Answer: I = 2.30^3 kg?m2 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 2.04m 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. I couldn't figure out the second two

Explanation / Answer

(b)
Torque = I * alpha, Torque = Tension * radius
Tension * radius = I * alpha
When the string is wrapped around the edge of the smaller disk, the radius is 0.0237 meter.

Tension * 0.0237 = I *alpha
I = 2.3 x 10-3
T * 0.0237 = 2.3 x 10-3 * alpha
T = (2.3 x 10-3 * alpha) / 0.0237
T = 9.7 * 10^-2 * alpha......................(1)

For the block, Net downward force = mass * a
The block has 2 vertical forces which affect its acceleration.
The tension in the string is the force is the upward force, and its weight is the downward force.

Weight = 1.5 * 9.8 = 14.7 N
Net downward force = 14.7 - T
14.7 - T = 1.5 * a
T = 14.7

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