- #1

ynbo0813

- 31

- 4

I=mr^2

A common derivation for this is:

1. F=ma

2. τ=rma

3. τ=rmrα = r^2 mα

This is a rotational version of Newton’s second law, where torque replaces force, moment of inertia replaces mass, and angular acceleration replaces tangential acceleration.

What bothers me is that the two rs in the formula refer to two different things: the r derived from torque (line 2) refers to the position where the force is acting; the r derived from angular acceleration (line 3) refers to the position of the mass. But what if the force is not acting on the same place as the mass? For example, what if a mass is placed on at point r from the pivot point, but the torque is applied at 2r from the pivot point. Does it have the same formula for its moment of inertia?