11.2 Newton’s laws, applied to rotation
As we have seen throughout this entire course, physical quantities dealing with translational motion tend to have analogous counterparts for rotation. We can think of two of Newton’s laws in terms of rotation:
- Inertia: an object’s rotational velocity will only change if it is acted on by some torque.
- The total torque acting on an object is equal to the rate of change of its momentum:
τnet = ΔL ⁄ Δt
If the moment of inertia of the system does not change, the total torque acting is equal to the object’s rotational inertia (moment of inertia) times its angular acceleration:
τnet = I α
Example
Newton’s third law does not directly apply to rotation. Consider that you need to apply a force to cause rotation; whatever object you are applying a force to is applying the same force back on you (Newton’s third law). However, the torque you exert on the object is not necessarily the same as the torque the object is exerting on you.
For example, say you exert some force F on a door by pushing a distance r from the door’s hinges. Your arm makes a 90° angle with the door. By Newton’s third law, the door exerts the same force F on you. However, the force the door exerts on you makes a 180° angle with your arm, because you are keeping your arm straight, and the door exerts the force directly into your hand. So while you exert some torque on the door, the door does not exert any torque on you (because sin(180°) = 0).
Newton’s third law is not being violated here—the door is exerting the same force on you that you exert on it—the third law just does not apply directly to torque.