Example of torque-free rotation with a fixed point

• Happiness
In summary, a rigid body rotating when one point is fixed and there are no net applied torques will have the same initial and final states.

Happiness

What is an example of a rigid body rotating when one point is fixed and there are no net applied torques? And the fixed point is not the center of mass.

I considered a cone rolling without slipping on a flat plane is such an example; the apex is the fixed point, but is there a net applied torque? I think there is.

Last edited:
The usual bike weel suspended off its com and precessing... there is no net torque because no net angular acceleration. Same with a tilted gyroscope. Though... suffers similar analysis issues as the cone.

... I need my whiteboard to check and I am stuck in hospital (Im fine).
(I imagine it is easy with lagrangian mechanics.)
But consider, if it completes a circle, then it has returned to its initial state (its trivial to rig), so the net work is zero. So I'll say there is no unbalanced torque... but may change my mind later.

___ where I am up to ____________
For analysis... a simplified verion is: a disk of unit circumference on one end of an axle... the other end of the axle is fixed to a pivot - the whole rests on a horizontal table. The length of the axel is such that the disk is constrained to a circle with N units circumference, must stay perpendicular to the axle which is so thin and light it has zero moment of inertia. The disk rolls on its edge without slipping and has non zero initial angular velocity. Sound good?

This means that the disk rotates exactly N times when it completes one circle... so initial and final states are totally the same (after one circuit, if angular velocity is constant) so no net work was done (no non conservative forces present).

Last edited:
Simpler yet... just an upright disk tethered to a pole at the z axis so it is contrained to move on a circle.
I think that has the features you want without the awkward mass distribution.

1. What is torque-free rotation with a fixed point?

Torque-free rotation with a fixed point is a type of rotational motion in which an object rotates around a fixed point without any external forces or torques acting on it. The object maintains a constant angular velocity and does not experience any change in its orientation.

2. What are some examples of torque-free rotation with a fixed point?

A common example of torque-free rotation with a fixed point is a spinning top. The top spins around its fixed point, which is the tip of the top, without any external forces acting on it. Another example is a planet orbiting around its star, where the star acts as the fixed point and the planet maintains a constant angular velocity.

3. How is torque-free rotation with a fixed point different from other types of rotational motion?

Torque-free rotation with a fixed point differs from other types of rotational motion in that it does not require any external forces or torques to maintain its motion. Other types of rotational motion, such as torque-induced rotation or precessional motion, require external forces or torques to initiate or maintain the motion.

4. What is the significance of torque-free rotation with a fixed point in physics?

Torque-free rotation with a fixed point is significant in physics because it is a fundamental concept in the study of rotational motion. It helps explain the behavior of objects in space, such as planets orbiting around a star, and also has practical applications in engineering and mechanics.

5. How is torque-free rotation with a fixed point related to angular momentum?

Torque-free rotation with a fixed point is closely related to angular momentum. In fact, the angular momentum of an object undergoing torque-free rotation with a fixed point remains constant, as there are no external torques acting on the object. This is known as the law of conservation of angular momentum.