Question

Two metal disks, one with radius R1= 2.60 cm and mass M1= 0.800 kg and the other with radius R2= 5.10 cm and mass M2= 1.70 kg, are welded together and mounted on a frictionless axis through their common center (Figure 1).

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 is suspended from the free end of the string. If the block is released from rest at a distance of 2.40 m above the floor, what is its speed just before it strikes the floor?

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

Answer 1

A.) The total moment of inertia of the two disks can be calculated by adding the individual moments of inertia. B.) The speed of the block just before it strikes the floor can be determined using the principle of conservation of mechanical energy. C.) When the string is wrapped around the larger disk, the moment of inertia of the system is different, and the speed of the block just before it strikes the floor can be calculated using the conservation of mechanical energy principle.

Step-by-step explanation:

A.) The total moment of inertia of the two disks can be calculated by adding the individual moment of inertia of each disk. The moment of inertia of a solid disk can be calculated using the formula I = (1/2) * M * R^2, where M is the mass and R is the radius. Thus, the moment of inertia of the first disk is I1 = (1/2) * 0.8 kg * (0.026 m)^2 and the moment of inertia of the second disk is I2 = (1/2) * 1.7 kg * (0.051 m)^2. Therefore, the total moment of inertia is I = I1 + I2.