Two metal disks, one with radius R1 = 2.44 cm and mass M1 = 0.820 kg and the oth

Question

Two metal disks, one with radius R1 = 2.44 cm and mass M1 = 0.820 kg and the other with radius R2 = 4.85 cm and mass M2 = 1.56 kg , are welded together and mounted on a frictionless axis through their common center. (Figure 1).

Part A

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

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Part 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 2.04 mabove the floor, what is its speed just before it strikes the floor?

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Part C

Repeat the calculation of part B, this time with the string wrapped around the edge of the larger disk.

Two metal disks, one with radius R1 = 2.44 cm and mass M1 = 0.820 kg and the other with radius R2 = 4.85 cm and mass M2 = 1.56 kg , are welded together and mounted on a frictionless axis through their common center. (Figure 1).

Part A

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

I =   kg?m2  

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Part 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 2.04 mabove the floor, what is its speed just before it strikes the floor?

v =   m/s  

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Part C

Repeat the calculation of part B, this time with the string wrapped around the edge of the larger disk.

v =   m/s  

Explanation / Answer

a) Total moment of inertia = 1/2 M1 R12 + 1/2 M2 R22

= (0.5 * 0.820 * 0.02442) + (0.5 * 1.56 * 0.04852)

= 2.08 * 10-3 kg.m2

b) v = sqrt [2 g h / [1 + (I/mR12)]]

= sqrt [2 * 9.8 * 2.04 / [1 + (2.08 * 10-3/1.50* 0.02442)]]

= 3.46 m/s

c) v = sqrt [2 g h / [1 + (I/mR22)]]

= sqrt [2 * 9.8 * 2.04 / [1 + (2.08 * 10-3/1.50* 0.04852)]]

= 5.0 m/s

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