A small disk of radius 0.5 m is mounted coaxially with a larger disk of radius 1

Question

A small disk of radius 0.5 m is mounted coaxially with a larger disk of radius 1.5 m. 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. The rotational inertia of the combination is 9.5 kg m2. A string is wrapped around the larger disk and attached to a block of mass 7, on the table. Another string is wrapped around the smaller disk and is pulled with a force 99 N along a tangential direction of the disk. Determine the acceleration of the block.

Explanation / Answer

Here

T=ma

-TR2+FR1=Ia/R2

maR2+Ia/R2=FR1

a=FR1/[mR2+(I/R2)]

a=99*0.5/[7*1.5+(9.5/1.5)

a=2.94 m/s2

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