I always thought that torque = I*d²θ/dt² so that, if there is any d²θ/dt² on an object with a moment of inertia (both with respect to the same point)..then there must be a torque applied. However, I've found a case where this isn't true. So, i'm assuming there is more to it then that simple formula. I found, on wiki "When the moment of inertia is constant, one can also relate the torque on an object and its angular acceleration in a similar equation: τ = I α " So perhaps, when the moment of inertia isn't constant, then that formula has some stuff appended to it. (what?) The situation i speak of: A particle is traveling in a straight line not through the origin at a constant velocity. It's (r) and (θ) are both functions of time. If you work out the time derivatives, you get a non-zero θ''. However, there are no forces, and no torques on the particle. (like a car just cruising past you). Also, the origin isn't moving or accelerating, so that there doesn't seem to be some relativity issue (i am not talking about special or general) Can anyone explain / tell me the full relation between torque and θ''...since torque = I*θ'' seems to be a simplified case.