20 November 2014: Conservation of Linear and Angular Momentum Lab 19

Objective:
The purpose of this lab is to investigate the conservation of angular momentum about a point that is external to a rolling ball. This differs from other labs since other labs looked at the angular motion of an object rotating about some internal axis.

This lab had three parts so it will be divided accordingly.
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Part 1:

The first set up was set up like this. A ball is slid down a ramp some height off the ground. It will then hit the ground at some point L away from the end of the ramp. A piece of carbon copy paper was placed on the floor to find exactly where the ball hit. This is a picture of the actual set up:




We measured that the ball landed .522 m away from the edge of the ramp. After we knew this distance, we were asked to find the launch speed of the ball.

Our calculations showed that the launch speed was 1.18 m/s.

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Part 2:

This part of the lab required the use of a rotational apparatus. This apparatus allowed tow disks to rotate freely. A ball would be launched from the ramp shown and caught by a little ball catcher attached to the top of a torque pulley on top of one of the rotating disks. Once the ball hit the ball catcher, the disk would begin to rotate. The point is to find out at what rotational speed the disk would rotate. But first, moment of inertia of the system must be found.

So first we put the rotating system in motion and to recorded data from its motion. From this data we were able to construct graphs that produced angular acceleration. The graphs can be seen below:

There is frictional torque acting on the system so the average of both angular accelerations will be taken: (5.934+5.339)/2= 5.637 rad/(s^2).

Now that we know angular acceleration we could find the moment of Inertia of the disk by these equations:

We then simply plugged in the known values of mass, radius of the torque pulley, and the above value of alpha to determine that the moment of inertia = .001057 kg*m^2.


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Part 3:
Now that the moment of inertia of the disk is known and the launch speed of the ball, we can find the rotational speed at which the disk will spin once the ball is caught. The calculations for this mainly used conservation of angular momentum and can be seen below:

So the angular momentum of the disk was 1.95 rad/sec.
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Conclusions:
The two parts of lab helped us find the value for the last part of the lab. From this lab we found that from launch speed kinematics and moment of inertia, we can find the rotational velocity of a real life disk in motion.