Rotational motion (conceptual error?)

[aspodkfpo]

Homework Statement

below

Relevant Equations

below

Very confused at this.

https://courses.lumenlearning.com/p...lisions-of-extended-bodies-in-two-dimensions/

"Consider the relatively simple collision shown in Figure 2, in which a disk strikes and adheres to an initially motionless stick nailed at one end to a frictionless surface. After the collision, the two rotate about the nail. There is an unbalanced external force on the system at the nail. This force exerts no torque because its lever arm r is zero. Angular momentum is therefore conserved in the collision. "

Can't see why the lever arm r is zero.

 

[etotheipi]

The origin of the coordinate system is set at the nail, and the system under consideration is the disk and the stick. The line of action of the reaction force from the nail on the stick passes through the origin of this coordinate system, so produces no torque.

 

[aspodkfpo]

The origin of the coordinate system is set at the nail, and the system under consideration is the disk and the stick. The line of action of the reaction force from the nail on the stick passes through the origin of this coordinate system, so produces no torque.

Don't quite understand what you mean. If its turning shouldn't the axis of rotation be at the nail in which case there is a lever? Is there torque in this scenario or not? Are they counting the rotation of the stick as an internal torque and talking about the nail on the stick reactive force as the external force?

 

[etotheipi]

The term "lever arm" just means the perpendicular distance between the line of action of a force and the chosen axis.

The disk and stick exert equal and opposite internal forces on each other, and the total torque of this pair about the axis of the nail is zero. The nail exerts an external force on the stick, but this reactive force has no torque about the axis of the nail (it's line of action has zero perpendicular distance to the nail!).