Question

A small disk of radius R1 is mounted coaxially with a larger disk of radius R2. The disks are securely fastened to each other and the combination is free to rotate on a fixed axle that is perpendicular to a horizontal frictionless table top, as shown in the overhead view below. The rotational inertia of the combination is I. A string is wrapped around the larger disk and attached to a block of mass m, on the table. Another string is wrapped around the smaller disk and is pulled with a force F as shown. The acceleration of the block is:

Answer 1

Answer:

Explanation:

For moment of inertia, the mass will appear as a point mass on the rim of the larger radius.

Total moment of inertia of the system is (I + mR₂²)

torque is FR₁

α = τ/I = FR₁/(I + mR₂²)

a = R₂α = R₂(FR₁/(I + mR₂²))

a = FR₁R₂/(I + mR₂²)