The centre of inertia (G) of a heterogeneous vehicle tyre has a distance D=0.1cm from its axis of rotation (the tyre's). The axis is referred to as Delta. The mass of the tyre is M=10kg and its radius is R=20cm. O is the center of the tyre (belongs to the axis)
Find the mass of an object (dot) X attached to the tyre so that the centre of inertia G is identical to the axis of rotation.
The Attempt at a Solution
This is what I've done so far, but with no avail:
I've considered G' as the centre of inertia of the whole group (the tyre and the object X), and G1 as the centre of inertia of X and "m" as its mass.
Therefore: Vector OG' = (m*vector OG1 + m*vectorOG) / m + M
I substituted G for O since we want it identical to the axis, which results into:
Vector OG' = (m*vector OG1 + m*vecto OO) / m + 10
Vector OG' = (m*vector OX) / m + 10 ( G1 = X itself)
Thus: OG' = (m*20) / m + 10
But I'm not sure where it's going to lead me. Please help me.