Is angular momentum perpendicular to fixed axis of rotation constant?

In summary, angular momentum is defined as the product of a body's rotational inertia and its angular velocity about a specific axis. When the axis of rotation is fixed and no external torques act on the system, the angular momentum remains constant and is indeed perpendicular to the axis of rotation. However, if external torques are present, angular momentum can change, even if the axis remains fixed. Thus, the constancy of angular momentum perpendicular to a fixed axis depends on the absence of external influences.
  • #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”?
 

FAQ: Is angular momentum perpendicular to fixed axis of rotation constant?

Is angular momentum always perpendicular to the axis of rotation?

No, angular momentum is not always perpendicular to the axis of rotation. It depends on the symmetry and constraints of the system. For a symmetric object rotating about a fixed axis, the angular momentum is typically along the axis of rotation. However, in more complex systems, angular momentum can have components that are not perpendicular to the axis of rotation.

What conditions are necessary for angular momentum to be perpendicular to the axis of rotation?

For angular momentum to be perpendicular to the axis of rotation, the system must be symmetric and the axis of rotation must be a principal axis of the object. Additionally, there should be no external torques acting on the system that could cause the angular momentum vector to deviate from being perpendicular.

How does external torque affect the angular momentum relative to the axis of rotation?

External torque can change both the magnitude and direction of angular momentum. If an external torque is applied, it can cause the angular momentum to precess, meaning it will not remain perpendicular to the axis of rotation. The relationship between torque and angular momentum is given by the equation \(\vec{\tau} = \frac{d\vec{L}}{dt}\), where \(\vec{\tau}\) is the torque and \(\vec{L}\) is the angular momentum.

Is angular momentum conserved if it is not perpendicular to the axis of rotation?

Angular momentum is conserved in a closed system with no external torques, regardless of its orientation relative to the axis of rotation. The direction and magnitude of angular momentum can change due to internal forces, but the total angular momentum of the system remains constant.

Can the angular momentum vector change direction while the axis of rotation remains fixed?

Yes, the angular momentum vector can change direction while the axis of rotation remains fixed, particularly in cases where the object is not symmetric or if there are external torques. This phenomenon is known as precession. For example, a spinning top exhibits precession where the angular momentum vector changes direction while the point of contact with the ground remains fixed.

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