Conservation of Angular Momentum in Collisions
Name____________________________________ Period_____
Purpose: The purpose of this lab is to test the Law of Conservation of Angular Momentum and to measure the
unknown speed of a projectile using this Law.
Setup Procedure: Divide the following three procedure steps among your group to maximize your efficiency.
1. Level the Rotational Apparatus Base. See Figure 2 below. Attach the rotating platform to the base making sure to
tighten the screw. Firmly attach the 300g square black mass to one end of the platform. Adjust the leveling screw on
one of the legs of the base until the end of the platform with the 300g mass is aligned over the other leveling screw.
Rotate the track 90o so it is parallel to one side of the “A” and adjust the other leveling screw until the platform will
stay in this position. Remove the 300g mass and check the level of the track by moving the platform. It should remain
at rest in any position.
2. Make sure the Smart Pulley is plugged into channel 1 of the Photogate Port and the Photogate Port is attached to the
USB Link and the USB Link is plugged into the computer. Start “Data Studio” and select “Smart Pulley Rotational”.
Remove the graph that comes up and then drag the Graph icon from the Displays window to the Velocity icon in the
Data window. You are now ready to record data.
3. Measure and record the various masses and dimensions of the lab equipment below. The Turntable and Ring are
over 1 kg. You must measure their mass on a balance that is set up and labeled for this. Use a regular balance for the
Platform mass. The Arrow must be measured accurately, use an electronic balance. Measure the average radius of the
ring. Measure rA from the center of the Platform to the screw securing the Arrow catcher.
Platform Mass (mP) = ________ kg
Arrow Mass (mA) = ________ kg
Turntable Mass (mT) = _______ kg
Ring Mass (mR) = _________ kg
Platform Length (lP) = _______ m
Distance from Arrow to Center of Platform (rA) = ________ m
Turntable Radius (rT) = _______ m
Ring Radius (rR) = _________ m
Arrow Experiment Procedure: 1. Make sure the arrow catcher is secure and perpendicular to the rotating platform and
almost at one of its ends.
2. Better data is obtained if one of the holes that allows the photogate beam to pass through is just about to enter the
beam. Rotate the platform so that the light on the photogate is off. Then slowly rotate it in the opposite direction it
will move when the arrow hits until the light just goes on.
3. Start recording with Science Workshop. Load an arrow and cock the gun by pulling out the handle below the grip.
Aim the arrow so it will move perpendicular to the rotating platform and horizontal to the floor. Fire the arrow into the
catcher from at least 5 cm away. Stop recording and record the first angular velocity value in the data table below.
Repeat two more times.
Arrow Experiment Analysis: 1. In this experiment angular momentum (L) is conserved from just before until just after
the collision of the arrow with the catcher. This means Li = Lf. Li is from the arrow since the platform is not
rotating initially. The angular momentum of a small object like the arrow moving in a straight line is mvr, where m is
the arrow’s mass, v is its velocity, and r is its distance to the rotation axis. Lf is the combined L of the platform and
the arrow after the collision. The L of an extended object is I where I is the total rotational inertia of the platform
and the arrow and  is their combined angular velocity before the platform slows down from friction. Derive an
expression for VA, the initial velocity of the arrow in terms of the platform and arrow mass and radii and the angular
speed. Show all of your work below. Use IP = mPlP2/12 and IA = mArA2. Use your equation and your measured values to
solve for the arrow’s velocity and record it in the data table below.
Trial
VA (m/s)
 (rad/sec)
1
2
3
Ring Experiment Procedure: 1. Remove the rotating platform by first loosening the screw underneath it. Attach the
turntable by lining up the notch in its center hole with the flat side of the axle.
2. Start recording and give the turntable a good torque to start it spinning. When the angular velocity is less than 25
rad/s, drop the ring into the groove on the turntable (Don’t Miss!). Stop recording and record the angular velocity just
before and after the ring is dropped in the table below. Repeat 2 more times.
Ring Experiment Analysis: Angular momentum is conserved from just before until just after the ring lands on the
turntable. Derive an expression for the final angular velocity, f in terms of mass and radius of the turntable and ring
and the initial angular velocity, i. Use IT = mTrT2/2. Show all of your work below. Use your expression and your
measured values to calculate f and record your results in the table below. Calculate the percent error and record it in
the table for each trial.
Tria
%
i
f Exp.
f Predicted
l
Error
(rad/sec)
(rad/sec)
(rad/sec)
1
2
3
Questions: 1. How would the angular velocity of the platform change if the arrow was shot at an angle other than 90 o?
Calculate the expected  if the arrow’s speed is 14 m/s and it is at an angle of 30o to the platform. Show all of your
work below.
30o
2. What would happen to the angular speed of the turntable if you quickly lifted the ring off it at the end of the second
experiment? Justify your answer.