Is angular momentum perpendicular to fixed axis of rotation constant?

  • #1
TahirMaqbool
16
1
TL;DR Summary
Does the component of angular momentum perpendicular to the fixed axis of rotation change in direction or magnitude?
So my book states torques perpendicular to the fixed axis of rotation tend to tilt the axis , however we assume sufficient restraints exist so these torques are simply ignored.
It follows that angular momentum perpendicular to axis remians constant.
(See image )

My question is that if a rod is hinged at one of its ends and allows to rotate, wouldn't angular momentum perpendicular to axis change in direction at each point?
See image below.
 

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  • #2
Are those “torques perpendicular to the fixed axis of rotation” also contained in the plane that is “perpendicular to the fixed axis of rotation”?
 

1. Is angular momentum perpendicular to fixed axis of rotation constant?

Yes, according to the conservation of angular momentum, the angular momentum of an object rotating around a fixed axis remains constant if there are no external torques acting on the system. This means that the angular momentum is perpendicular to the fixed axis of rotation and remains constant throughout the motion.

2. How does angular momentum relate to the fixed axis of rotation?

Angular momentum is a vector quantity that is perpendicular to the fixed axis of rotation. It is defined as the cross product of the position vector and the linear momentum of the object. This means that the direction of angular momentum is always perpendicular to the plane formed by the position vector and the linear momentum vector.

3. What happens to angular momentum if there are external torques acting on the system?

If there are external torques acting on the system, the angular momentum of the object rotating around a fixed axis may not remain constant. In this case, the angular momentum will change in magnitude and direction as the external torques cause the object to accelerate or decelerate in its rotational motion.

4. Can the direction of angular momentum change in a rotating system?

Yes, the direction of angular momentum can change in a rotating system if there are external torques acting on the system. The angular momentum will always be perpendicular to the fixed axis of rotation, but its direction can change as the object accelerates or decelerates due to external torques.

5. How is angular momentum conserved in a rotating system?

Angular momentum is conserved in a rotating system when there are no external torques acting on the system. This means that the total angular momentum of the system remains constant throughout the motion, even though the individual angular momenta of the objects in the system may change. Conservation of angular momentum is a fundamental principle in rotational dynamics.

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