Torque about an accelerating axis

[tachyontensor]

How are torques computed about an axis when the axis (and the attached body) are both accelerating at the same rate? For example, if a car is in free fall with the doors open (with the rear end of the car pointing towards the ground) will the doors shut themselves due to torque? Or, is the torque zero because the axis and door(s) are moving uniformly?

Also, in a more general sense, if several objects are in the same accelerating reference frame, can a "pseudo" form of Newton's laws (adjusted for the fictitious forces) hold for all objects in the frame?

This isn't homework, just a curiosity.

 

[Shooting Star]

The torque about any point O due the force F acting through P is defined as OPXF. We use this all the time when studying the motion of wheels rolling down inclined planes etc. if O is the door hinge and P is any point on the door, then it may seem a bit counter intuitive to notice that the vector OP remains constant, since both P and O fall at the same rate, and therefore the torque is constant. However, the angular momentum about any instantaneously stationary horizontal axis passing through O is also increasing due to the increasing speed of the point P, and there is no contradiction.

The car door in your example will not swing shut since the whole car is in free fall, and effectively there is no gravity in the car frame.

In mechanical problems, in general we have to make one of the following choices:

1. Select an initial frame and consider only the “real” forces.
2. Select a non-inertial frame and consider not only the “real” forces, but suitably defined pseudo or fictitious forces.

In the falling car example, the addition of the force (–mg ) to a particle of mass m makes the frame compatible with Newton’s laws of motion. Another example is a rotating frame, where you have to take into account the centrifugal and the Coriolis forces, and then start to use Newton's laws again.

 

[astrokreng]

I can provide a response to the concept of torque about an accelerating axis. Torque is a measure of the rotational force applied to an object, and it is computed by multiplying the force applied to the object by the distance from the axis of rotation. In the case of an accelerating axis, the torque can still be computed using this formula, but it may be more complex due to the added acceleration.

In the example given, if a car is in free fall with the doors open, the doors will not shut themselves due to torque. This is because the torque is zero in this situation, as both the axis (the car's center of mass) and the doors are accelerating at the same rate. This means that there is no rotational force being applied to the doors, and they will remain open.

In a more general sense, if several objects are in the same accelerating reference frame, a "pseudo" form of Newton's laws can hold for all objects in the frame. This is because in an accelerating reference frame, fictitious forces (such as centrifugal force or Coriolis force) need to be taken into account when applying Newton's laws. These forces are not real forces, but rather appear to exist due to the acceleration of the reference frame. By adjusting for these fictitious forces, Newton's laws can still be applied to all objects in the frame.

I hope this helps to satisfy your curiosity. It is always important to consider the effects of acceleration when applying physical laws, as it can greatly impact the behavior of objects.