The angular momentum of a rotating rigid body rotating about a fixed axis is defined to be

where I is the moment of inertia of the body about its axis and is the angular velocity of the body. The purpose of this experiment is to investigate the conservation of angular momentum in collisions between rotating discs.

Use the rotational dynamics apparatus with the air pressure set to 9 psi unless otherwise stated.

1. Initially use the two steel discs with the drop pin placed through the top disc so that the two discs can rotate independently
2. Hold the bottom disc stationary and spin the top disc until a frequency of at least 300 Hz is obtained. Wait 2 seconds and then make a reading of the frequency of the top disc
3. Release the bottom disc and immediately pull the drop pin so that the two discs collide. Wait two seconds then record the frequency again.
4. Convert the two frequencies to angular velocities and by calculating the moment of inertia of each of the discs find the angular momentum of the system before and after the collision.
5. Check if momentum is conserved. Check if kinetic energy is conserved. If these quantities are not conserved give the percentage change and explain why they are not conserved.
6. Repeat the above experiment spinning the top disc at a significantly different initial angular velocity.
7. Repeat the above experiment spinning the bottom disc with an angular velocity opposite to that of the top disc. You will need to read the initial frequency of both the top and bottom discs before allowing them to collide. Remember also that when you check for conservation of angular momentum that angular momentum is a vector quantity.
8. Repeat the above experiment replacing the steel top disc with the aluminium top disc (set the air pressure to 6 psi)

Although the air pressure allows this experiment to proceed with minimal error due to energy losses you should observe that over time the discs slow down. This apparatus can be used to find a quantitative relationship between the kinetic energy and time for a rotating body under the influence of friction. Rotate the top disc at a frequency of at least 300 Hz and allow the Logger Pro to record the frequency for about 5 minutes. Convert the frequencies to angular velocity and then to kinetic energy using the Lab pro software. What is the relationship between kinetic energy and time? (Is it linear or exponential or does it follow some power law?) How long does it take for half the energy to be lost? Does this time depend on what the initial energy is? Use your plot to estimate the percent of energy lost in the above collision experiments.

While the other groups are working with the rotational dynamics apparatus you can investigate angular momentum in toys and other systems:

When the axis of rotation of a spinning object is not vertical and the pivot point is not at the centre of mass then it will feel a net torque due to gravity. This torque will be in a direction perpendicular to the angular momentum and as such will cause the direction of the angular momentum to change, but will not change its magnitude. As a consequence the axis of rotation (the direction of the angular momentum) will slowly revolve around the pivot point in the direction of the torque but the angular velocity of the spinning top will remain unchanged. This phenomenon is known as precession. Your task in this experiment is to gain a qualitative understanding of precession. Spin the gyroscope and hang it from a piece of string so that the axis of rotation is horizontal. Describe its motion. Try varying the spinning frequency and both in magnitude and direction. How is the precession frequency ω_p (rotation of axis around pivot) related to the spinning frequency ω (rotation of gyroscope about axis)? Can you predict the direction of precession if you know the direction of the spin (Use the right hand rule)? Change the angle of the axis or rotation so that it is above the vertical. How does the angle of the axis of rotation affect the magnitude of ω_p?

When a yo-yo is released it is subject to a net torque. This torque increases the magnitude of the angular momentum. As the yo-yo spins up and down describe how the angular momentum changes. Does the direction of angular momentum vector stay constant? Sketch a graph of angular momentum as a function of height. Compare the accelerations of the yo-yo, an object in free fall, a spool coiled with thread and Maxwell's wheel. Explain any differences you observe. Is the acceleration of the Yoyo uniform? (How could you check?).

Spin the doodle top and describe carefully the pattern you observe and explain it physically. Is the angular momentum of the top conserved? If not why not? Does the angular momentum vector always point in the same direction? Explain any changes you observe.

Spin the Chinese bouncing top. How many forms of energy does it possess?

Spin the orbiter. How does it change shape when you spin it fast. In what way does the moment of inertia of the orbiter change when it changes shape? If angular momentum is conserved for the orbiter should this change result in an increase or decrease in angular speed? Read the description of the physics of the orbiter on the package and give a critique. If you worked for a toy manufacture would you write a description like that?