A string is wrapped around a uniform solid cylinder of radius , as shown in the

Question

A string is wrapped around a uniform solid cylinder of radius , as shown in the figure (Figure 1) . The cylinder can rotate freely about its axis. The loose end of the string is attached to a block. The block and cylinder each have mass . We are going to pretend that we don't know the formula for the rotational inertia for the cylinder and instead, use the block's measured acceleration to figure out the rotational inertia of the cylinder. Note that the positive y direction is upward and counterclockwise torques are positive. Part A The block has two forces acting on it: the tension of the string and its own weight. What is the net force acting on the block? Use the coordinate system shown in the figure.

Explanation / Answer

from Newton’s law, mg-T = ma, a = r -----------(1)

For the pulley = I

that is Tr = 1/2 m r2

T = 1/2mr ------------(2)

Plug in equation (1)

mg – 1/2mr =mr

= 2g/3r

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