Question

Why is the radius or distance from axis of rotation squared as in \[I = mr_{cm}^2 \]

Answer 1

its a rotational analogue to mass (inertia) drawn from the equation for torque

Answer 2

F=ma
T=Fr
Fr = mar
a=r(alpha)
hence
T=mr^2 (alpha)

Answer 3

T is to force what alpha is to a, hence the analogue of mass is the moment of inertia (mr^2)

Answer 4

this is because in rotational mechanics the mass is equivalent to the moment of inertia. and the term r is squared because I is moment of inertia and the axis of rotation if taken along some axis then the distance should be positive. theoretically...