Consider a system like the example problem where a batting machine swings a bat but instead of a baseball, the bat hits a lump of clay, which sticks to the end of the bat. How does the angular momentum of the clay and bat after the collision compare to the angular momentum of the clay and bat before the collision, and why?
It increases, the mass of the rotating object increases
It decreases, the velocity of the rotating object decreases
It decreases, momentum is lost in the collision
It stays the same, there is no external torque on the system
I said that it decreases because momentum is lost...that was wrong...
Assuming that the collision happened so fast that the machine swinging the bat put no work in during the collision the angular momentum (of the entire bat/clay system)does not change. The moment of inertia is a little higher due to the mass of the clay so the angular velocity slows a bit, but the Angular momentum is the same before and after. Remember that not only the bat but the clay as well had angular momentum before the collision.
The correct answer is: It stays the same, there is no external torque on the system.
Angular momentum is a property of a rotating object and is given by the product of its moment of inertia and its angular velocity. In the given scenario, the lump of clay sticks to the end of the bat, which means it becomes a part of the system and rotates with the bat.
Since there is no external torque exerted on the system (i.e., no external force causing the system to rotate faster or slower), the angular momentum of the system is conserved. Therefore, the angular momentum of the clay and bat after the collision will be the same as the angular momentum before the collision.
To determine how the angular momentum of the clay and bat after the collision compares to the angular momentum before the collision, we need to consider the conservation of angular momentum.
Angular momentum is defined as the product of the moment of inertia and the angular velocity. In this case, the moment of inertia is dependent on the mass distribution and shape of the object being rotated (the bat and clay), while the angular velocity is the rate at which the object is rotating.
In the absence of any external torques acting on the system, the total angular momentum before the collision should be equal to the total angular momentum after the collision. This is known as the conservation of angular momentum.
However, in this scenario, the lump of clay sticks to the end of the bat after collision. This means that the mass distribution of the rotating system changes. As a result, the moment of inertia of the system is altered.
Since the moment of inertia changes and we assume no external torque acts on the system, the initial angular momentum is different from the final angular momentum. Therefore, the correct answer is:
It stays the same, there is no external torque on the system.
In this case, even though the mass distribution changes, the stickiness of the clay doesn't introduce any external torques that would cause a change in the total angular momentum of the system.