Lab 1: Conservation of Angular Momentum: Rotational Collisions
In this lab, you will verify the law of conservation of angular momentum by colliding a rotating disk with a stationary disk and a stationary rectangular object. In this lab, the disk and rectangular slab will rotate about their center of mass.
Background
Conservation laws are very important in physics. So far you have seen conservation of energy and conservation of linear momentum. It turns out that a new quantity, angular momentum, is also conserved. Just like linear momentum, which is conserved when there are no external forces acting on the system, angular momentum is conserved when there are no net external torques acting on the system.
For a rigid body, angular momentum (L) can be written as,
where I is the rotational inertia (or moment of inertia) of the rigid body, and omega is the angular velocity of the body. The rotational inertia is a measure of how difficult it is to rotate an object. The rotational inertia of different rigid bodies is given in your textbook. This is analogous to translational inertia (or mass). The more massive an object the more difficult it is to get it to move.
When a quantity is conserved, this quantity does not change over time. Stated mathematically for angular momentum, where L before is the angular momentum before the collision and L after is the angular momentum after the collision.
Purpose
The collision entails rotating the disk on the rotational apparatus and then dropping (not
from too high!) the second object onto the rotating disk. The goal here is to verify that
angular momentum is conserved.
You need to calculate the angular momentum before the collision and after the collision for two cases. Case I: Collide rotating disk with stationary disk. Case II: Collide rotating disk with stationary rectangle. This means you need the rotational inertia and angular velocity before the collision and after the collision for both cases.
Procedure/Analysis
Measuring the Angular Velocity
To measure the angular velocity we will use a photo-gate detector. In general, this
detector will measure the time it takes for an object to go between its sensor. A
cardboard strip taped to your rotating disk will pass through the sensor. The sensor will
record the time it takes the cardboard strip to pass through the sensor. How can you find
the angular velocity with this information? (Hint: You need a relationship between linear
velocity and angular velocity.)
Measuring the rotational inertia of the different objects
A formula for the rotational inertia for different objects can be found in your textbook. Measure the mass and relevant dimensions of the objects so that you can calculate I for each. The spool that holds the disk onto the rotational apparatus also has rotational inertia, estimate this.
Make sure you answer the following in your lab report.