Consider a rotating platform such as you used in lab. Imagine that it is initially rotating at some angular velocity.
You drop a disk, that is not rotating, onto the top of the rotating platform so that it sticks to the rotating platform and begins rotating along with the rotating platform. The center of the disk coincides with the rotation axis. Assume that the disk has a significant moment of inertia around the rotation axis of the platform, i.e. the z-axis.
For this rotational collision, which of the following should you observe for the total rotating system (platform + object)?
The angular velocity, after the collision, is smaller.
The total angular momentum of the system is constant.
The angular velocity, after the collision, is the same.
The angular velocity, after the collision, is larger.
The kinetic energy of the system is constant.
The total energy of the system is constant.
-total energy
-total angular momentum
-angular velocity is smaller
To analyze what you should observe for the total rotating system (platform + object) after the collision, we need to consider the concept of conservation of angular momentum.
Angular momentum is a measure of an object's rotational motion and is defined as the product of its moment of inertia and angular velocity. In this case, the rotating platform has an initial angular velocity, and when you drop the disk onto it, the disk starts rotating with the platform.
During the collision, there are no external torques acting on the system (assuming no friction or other external forces), which means the total angular momentum of the system should be conserved.
Now, let's consider the options:
1. The total angular momentum of the system will decrease: This cannot happen because angular momentum is conserved in the absence of external torques. The angular momentum of the rotating platform will be transferred to the disk, effectively increasing the total angular momentum of the system.
2. The total angular momentum of the system will increase: This is the correct answer. As stated earlier, the angular momentum of the rotating platform will transfer to the disk when it is dropped onto the platform. This transfer of angular momentum will increase the total angular momentum of the system.
3. The total angular momentum of the system will remain the same: This cannot happen, as the angular momentum of the platform is transferred to the disk during the collision, resulting in an increase in the total angular momentum of the system.
Therefore, you should observe an increase in the total angular momentum of the system (platform + object) after the collision.