Question

A 10kg block is attached to a massless cord that doesn't stretch or sag which is rapped around a disc like wheel, m=5Kg, I= (1/2)mR^2. If the block is allowed to drop straight down held back only by the rotation of the wheel:

1. What is the tension of the rope?
2. What is the acceleration of the block?

Answer 1

The force on the rope is tension, which is equal to mg-ma

But this same tension is spinning the wheel:

angularacceleration=Tension/I
a/R=Tension/I

aI=R(mg-ma)
solve for a, then you have it.

check my thinking.