A uniform, 4.5-kg, square, solid wooden gate 1.5 m on each side hangs vertically from a frictionless pivot at the center of its upper edge. A 1.1-kg raven flying horizontally at 5.0 m/s flies into this door at its center and bounces back at 2.0 m/s in the opposite direction. (b) During the collision, why is the angular momentum conserved but not the linear momentum?

Verified step by step guidance

1. Identify the system for which the conservation laws are being analyzed. In this case, the system includes the wooden gate and the raven.
2. Understand that linear momentum is not conserved because there are external forces acting on the system. The pivot at the top of the gate exerts an external force to ensure the gate remains in place, thus affecting the linear momentum of the system.
3. Recognize that angular momentum is conserved because the external forces (from the pivot) act at the pivot point itself, which is the axis of rotation. Since the force has no lever arm with respect to the axis, it exerts no torque, and thus does not affect the angular momentum.
4. Consider the initial and final states of the system. Initially, the gate is at rest and the raven is moving, and finally, the gate might be rotating and the raven has reversed its direction. The change in motion of the raven and any resulting motion of the gate must conserve angular momentum about the pivot.
5. Apply the principle of conservation of angular momentum to calculate any unknowns in the problem, such as the angular velocity of the gate post-collision, by setting the initial angular momentum equal to the final angular momentum.

Key Concepts

Angular Momentum

Angular momentum is a measure of the rotational motion of an object and is defined as the product of the object's moment of inertia and its angular velocity. In this scenario, the gate's pivot allows it to rotate, and the collision with the raven affects its angular momentum. Angular momentum is conserved in a closed system where no external torques act, which is the case here since the pivot is frictionless.

Linear Momentum

Linear momentum is the product of an object's mass and its velocity, representing its motion in a straight line. In this situation, the raven collides with the gate, and while the raven's momentum changes, the gate's initial linear momentum is zero. The system is not closed for linear momentum because the gate can exert a force on the raven, and external forces can influence the overall linear momentum during the collision.

Conservation Laws

Conservation laws in physics state that certain quantities remain constant in isolated systems. The conservation of angular momentum applies here because the system (gate and raven) does not experience external torques during the collision. However, linear momentum is not conserved due to the interaction forces between the raven and the gate, which can change the total linear momentum of the system.