CONSERVATION OF ANGULAR MOMENTUM
In this experiment, we first study the relationship between torque, moment of inertia and
angular acceleration, using a rotating platform. We then test the law of conservation
of angular momentum by analyzing inelastic collisions between rotating objects.
1 rotating platform with photogate,
1 pulley with clamp,
1 iron disk with handle,
1 interface box,
1 computer with timing program,
Observing the angular acceleration of an object, the rotating platform, under an external torque
will enable us to measure the moment of inertia of the object, using the equation
is the net external torque,
is the angular acceleration, and
is the moment of
inertia. After the moment of inertia is determined, conservation of angular momentum will be
investigated by dropping a mass onto the rotating platform, and measuring the angular velocity
before and after the "drop." The equation
is an expression of the conservation of
angular momentum for this system, with the subscripts
referring to the initial and final
states. This rotational inelastic collision is completely analogous to the linear inelastic collision
studied last week on the air track.
I. Correction for Systematic Error, i.e., Friction
Unlike the motion of the glider on the air track, the rotating table does exhibit significant
friction. After starting its rotation, the table will slow down and eventually stop. However,
this effect can be taken into account by a preliminary experiment. Set up the computer in
MOTION TIMER mode and measure the angular velocity
of the freely turning table for 20 or
30 seconds. When the program requests the distance between timings, enter the angular distance
(in radians) between the pieces of tape on the plastic ring that pass through the photogate. The
velocities will then be in radians/sec.
Q1. How does the angular velocity change as time progresses? Graph
book. If you can, fit a straight line to your data points and
calculate the slope.
Q2. Is the frictional torque dependent on the velocity?
Q3. How does the slope relate to the angular acceleration,