- #1
Albertgauss
Gold Member
- 292
- 37
Hi all,
Here is what I am trying to understand qualitatively. It is NOT a homework problem:
A long, one-dimensional rod of mass M and length L is in free space. There is no gravity, no forces, and no pivot. Its just a rod sitting there, floating, with nothing else around. Let's say its L=0 end is at the origin (y=0), and its L=L end at a positive y=L. Suppose I strike the y=L end of the stick in the +X direction. By Newton's Inertial Law, the stick should move translationally as I transferred momentum to it. But will it spin? I can't figure that out.
I thought perhaps that it might. I tried to think of the stick as comprised of many atoms attached to each other by springs. I made some simplifying assumptions. The atoms at the y=L of the stick that receive the WHACK will experience a force via an impulse in the pure positive X direction as long as I am in contact (however brief) with the y=L end. The atoms at the y=L end will also experience a restoring force due to their neighboring atoms trying to pull them back. That restoring force would point towards the third quadrant. The restoring force and my impulse force would produce a net force pointing towards the fourth quadrant, and hence I would have a clockwise torque. Thus, I would conclude the rod will indeed spin as it moves off.
How am I doing?
Here is what I am trying to understand qualitatively. It is NOT a homework problem:
A long, one-dimensional rod of mass M and length L is in free space. There is no gravity, no forces, and no pivot. Its just a rod sitting there, floating, with nothing else around. Let's say its L=0 end is at the origin (y=0), and its L=L end at a positive y=L. Suppose I strike the y=L end of the stick in the +X direction. By Newton's Inertial Law, the stick should move translationally as I transferred momentum to it. But will it spin? I can't figure that out.
I thought perhaps that it might. I tried to think of the stick as comprised of many atoms attached to each other by springs. I made some simplifying assumptions. The atoms at the y=L of the stick that receive the WHACK will experience a force via an impulse in the pure positive X direction as long as I am in contact (however brief) with the y=L end. The atoms at the y=L end will also experience a restoring force due to their neighboring atoms trying to pull them back. That restoring force would point towards the third quadrant. The restoring force and my impulse force would produce a net force pointing towards the fourth quadrant, and hence I would have a clockwise torque. Thus, I would conclude the rod will indeed spin as it moves off.
How am I doing?