Understanding the Rotation of a Freefalling Rod

In summary: Problem assumes uniform gravitational field. There are no tidal forces. Doc Al and A.T. have it covered from both...
  • #1
aaaa202
1,169
2
This has been brought up numerous times but I don't really understand it. Consider a rod in freefall.
If you put your coordinate frame in the center of mass of the rod, there will be no torque around it and the rod as a whole will follow a straightline down. But now put a coordinate frame on one of the end points. Apart from the gravity pulling down on the rod as a whole, there will now be a net torque on the rod (because gravity acts in the center of mass).
What goes wrong with this picture, because clearly the rod doesn't rotate!
 
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  • #2
aaaa202 said:
This has been brought up numerous times but I don't really understand it. Consider a rod in freefall.
If you put your coordinate frame in the center of mass of the rod, there will be no torque around it and the rod as a whole will follow a straightline down. But now put a coordinate frame on one of the end points. Apart from the gravity pulling down on the rod as a whole, there will now be a net torque on the rod (because gravity acts in the center of mass).
What goes wrong with this picture, because clearly the rod doesn't rotate!

the rod is a rigid body. the other side of the rod also has an equal torque, and due to rigidity, will be in the opposite direction.
 
  • #3
aaaa202 said:
This has been brought up numerous times but I don't really understand it. Consider a rod in freefall.
If you put your coordinate frame in the center of mass of the rod, there will be no torque around it and the rod as a whole will follow a straightline down. But now put a coordinate frame on one of the end points. Apart from the gravity pulling down on the rod as a whole, there will now be a net torque on the rod (because gravity acts in the center of mass).
What goes wrong with this picture, because clearly the rod doesn't rotate!
The problem is that you are you using an accelerating point as your 'pivot'. Torque about such an accelerating point does not simply equal the rate of change of angular momentum, unless that point happens to be the center of mass.

See my post in this thread: https://www.physicsforums.com/showthread.php?p=4097976
 
  • #4
chill_factor said:
the rod is a rigid body. the other side of the rod also has an equal torque, and due to rigidity, will be in the opposite direction.
The only external force acting on the rod is gravity.
 
  • #5
aaaa202 said:
But now put a coordinate frame on one of the end points. Apart from the gravity pulling down on the rod as a whole, there will now be a net torque on the rod (because gravity acts in the center of mass).
In an accelerated frame that falls with the rod, there is an inertial force upwards:
http://en.wikipedia.org/wiki/Fictitious_force#Acceleration_in_a_straight_line

The inertial force cancels gravity at any point of the rod. Regardless if the origin is in the center or the end: There is no net force on any part of the rod in such a frame, and thus no torque.
 
  • #6
A.T. said:
The inertial force cancels gravity at any point of the rod. Regardless if the origin is in the center or the end: There is no net force on any part of the rod in such a frame, and thus no torque.
That's a good way to look at it (and probably more straightforward).

The extra terms (beyond the torque due to external forces) you get when you calculate dL/dt about an accelerating point are equivalent to introducing that inertial force.
 
  • #7
In the frame of one of the ends, the rod gains angular momentum - by falling linearly to the floor.
The torque is present, and required for a linear motion downwards in this frame.
 
  • #8
mfb said:
In the frame of one of the ends, the rod gains angular momentum - by falling linearly to the floor.
The torque is present, and required for a linear motion downwards in this frame.
Viewed from an inertial frame, the rod gains angular momentum. But in the accelerating frame of one of its ends, it does not.
 
  • #9
A.T. said:
The inertial force cancels gravity at any point of the rod. Regardless if the origin is in the center or the end: There is no net force on any part of the rod in such a frame, and thus no torque.
Yes, there is a torque. It's the same phenomenon that causes spaghettification. Taking advantage of, or otherwise dealing with, gravity gradient torque is an important concept for satellites in low Earth orbit.
 
  • #10
D H said:
Yes, there is a torque. It's the same phenomenon that causes spaghettification. Taking advantage of, or otherwise dealing with, gravity gradient torque is an important concept for satellites in low Earth orbit.
Problem assumes uniform gravitational field. There are no tidal forces. Doc Al and A.T. have it covered from both perspectives.
 

1. What is the concept of rotation in physics?

The concept of rotation in physics refers to the circular movement of an object around a fixed point or axis. This movement can either be uniform, where the object moves at a constant speed, or non-uniform, where the object changes its speed or direction during rotation.

2. How does gravity affect the rotation of a freefalling rod?

Gravity is the force that pulls objects towards the center of the Earth, and it also plays a significant role in the rotation of a freefalling rod. As the rod falls, gravity causes it to rotate around its center of mass, creating a spinning motion.

3. What is the difference between rotational and translational motion?

Rotational motion refers to the movement of an object around a fixed point or axis, while translational motion refers to the movement of an object from one point to another in a straight line. In the case of a freefalling rod, both rotational and translational motion are present as the rod falls and rotates simultaneously.

4. How does the shape of a freefalling rod affect its rotation?

The shape of a freefalling rod can have a significant impact on its rotation. A longer and more massive rod will experience more resistance to rotation, making it rotate slower than a shorter and lighter rod. Additionally, the distribution of mass along the rod's length can also affect its rotation.

5. What factors can influence the stability of a freefalling rod's rotation?

The stability of a freefalling rod's rotation can be influenced by several factors, including the shape and mass distribution of the rod, the speed at which it falls, and external forces such as air resistance. In general, a more symmetrical and evenly distributed rod will have a more stable rotation compared to an asymmetrical or unevenly distributed one.

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