- #1
Farina
- 39
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More specifically... question stumps 3 physics profs, PF, textbooks, and entire Internet.
It’s easy to find explanations of why a gyroscope precesses. What’s not so easy to find – even after spending, literally, hours thinking about it, surfing the web (including PhysicsForums), reading textbooks, and asking physics instructors with PhDs, is this: in terms of torque, torque arms, angular momentum, right-hand rules, cross products, and – especially – simple force equilibrium analysis, WHY DOES A SPINNING GYROSCOPE LEVITATE?
Here’s, specifically, how I’m stumped:
Take a toy gyroscope or equivalently a bicycle wheel gyroscope (I’m using both). Orientate the gyroscope so its axis of rotation is horizontal. Suspend one end of the axis by a rope, hold the other end of the axis with your hand – keeping it horizontal. Remove your hand, and of course the gyroscope falls and is left dangling on the rope with its axis now vertical. Now repeat with a spinning gyroscope. This time when you let go the gyroscope remains horizontal as it precesses. As framed by the following, WHY DOES A SPINNING GYROSCOPE LEVITATE?
For a non-spinning gyroscope…
Tension force from the string acts on one end of the wheel’s axis of rotation in the +y direction. A gravitational force acts on the COM in the –y direction. The negative y-forces are greater than the +y forces, as evidenced by the COM moving downward – thus the gyroscope flops over.
For a spinning gyroscope…
Same +y tension force, same –y gravitational force, but now there must be an additional +y force since the gyroscope exhibits no net vertical displacement, like it did when it was not spinning (its COM now remains in the same horizontal plane). Here’s the big question: what is the genesis of this new +y force? What gives rise to it in terms of underlying torques, torque arms, angular momentum, right-hand rules, cross products, etc., etc.
Thanks for any insight.
It’s easy to find explanations of why a gyroscope precesses. What’s not so easy to find – even after spending, literally, hours thinking about it, surfing the web (including PhysicsForums), reading textbooks, and asking physics instructors with PhDs, is this: in terms of torque, torque arms, angular momentum, right-hand rules, cross products, and – especially – simple force equilibrium analysis, WHY DOES A SPINNING GYROSCOPE LEVITATE?
Here’s, specifically, how I’m stumped:
Take a toy gyroscope or equivalently a bicycle wheel gyroscope (I’m using both). Orientate the gyroscope so its axis of rotation is horizontal. Suspend one end of the axis by a rope, hold the other end of the axis with your hand – keeping it horizontal. Remove your hand, and of course the gyroscope falls and is left dangling on the rope with its axis now vertical. Now repeat with a spinning gyroscope. This time when you let go the gyroscope remains horizontal as it precesses. As framed by the following, WHY DOES A SPINNING GYROSCOPE LEVITATE?
For a non-spinning gyroscope…
Tension force from the string acts on one end of the wheel’s axis of rotation in the +y direction. A gravitational force acts on the COM in the –y direction. The negative y-forces are greater than the +y forces, as evidenced by the COM moving downward – thus the gyroscope flops over.
For a spinning gyroscope…
Same +y tension force, same –y gravitational force, but now there must be an additional +y force since the gyroscope exhibits no net vertical displacement, like it did when it was not spinning (its COM now remains in the same horizontal plane). Here’s the big question: what is the genesis of this new +y force? What gives rise to it in terms of underlying torques, torque arms, angular momentum, right-hand rules, cross products, etc., etc.
Thanks for any insight.