Angular Momentum

Purpose 

To determine the height the meter stick reaches after colliding with the clay through using the conservation of energy and momentum and doing it experimentally. 

Procedure + Lab Equipment

What we used:

• meter stick
• clay
• video camera
• logger pro
• ring stand

What we did:

1. we took measurements of the meter stick and clay
2. we calculated how how the meter stick would reach after collision
3. we set the meter stick on the ring stand and the clay at the appropriate spot 
4. we used the video camera to record a video to analyze how high the meter stick actually reached

Data

(M) mass of meter stick: 0.083 kg

(m) mass of clay: 0.01592 kg

(H) initial height: 1.135 m (this is when the meter stick is parallel with the floor)

Data Analysis + Calculations 

These are the calculations for the expected height that the meter stick will reach 
We expect the meter stick to reach a height of 0.6045 m

This is the video analysis for the experimental height the meter stick reached
The y-axis gives us the height reached, which is 0.7642 m

Summary

In our lab, we used the conservation of energy and momentum to help us determine the height that the meter stick would reach after colliding with the clay. Our calculated height was 0.6045 m while our experimental height was 0.7643m. Our percent error was about 26%, more than the accepted value. 

What might have gone wrong in the experiment is that the meter stick didn't start exactly at the end, we also didn't measure the initial height for this video capture. What we did was measure the initial height once when it was horizontal, but not through each video capture. We also don't account for friction or air resistance as the meter stick swings.

Triangle's Moment of Inertia (about its center of mass)

Purpose

In this lab, we were looking to find the moment of inertia of a triangle about its center of mass

Procedure + Lab Equipment

What we used:

• rotating apparatus
• disks
• hanging mass
• torque pulley
• hanging mass
• triangle
• holder for triangle
• caliper to measure

 What we did:

1. we took measurements of the triangle
2. we set the rotating apparatus with a hanging mass took angular acceleration of the rotating apparatus without the triangle, with the triangle on its base, and on its height
3. we calculated the moment of inertia by experiment using angular acceleration and by calculations using calculus

 

This is the setup for the disks and holder only

This is the setup for when the triangle is on its base

This is the setup for when the triangle is on its height

Data

This is the angular acceleration for the disks with the holder

Data Analysis + Calculations

Calculations for the moment of inertia of a triangle about its center when its on its base

 

Calculations for the moment of inertia of a triangle about its center when its on its height

Moment of Inertia

Angular Acceleration

Purpose

We are looking at how the angular acceleration is affected by changing the:

• hanging mass
• torque pulley
• disks
  

Procedure + Lab Equipment

What we used:

• rotating apparatus
• aluminum disk
• steel disk (2)
• small torque pulley
• large torque pulley 
• hanging mass
•  caliper to measure disk + pulley diameters
• logger pro

What we did:

1.  took measurements of the disks and pulleys
2. set up the apparatus 
1. cleaned the disks with alcohol
3. set up logger pro
• sensor set to rotary motion
• data set to 200 counts per rotation
4. turned the compressed air on
• check to see if everything's in order
5. let the hanging mass go 
• collect data

Data

The slopes of each graph were found to determine the angular acceleration. These were from using the small pulley.

The slopes of each graph were found to determine the angular acceleration. These were from using the large pulley.

These are the angular accelerations for each experiment

 Data Analysis + Calculations

Hanging Mass

When we look at experiments 1, 2, and, 3, the hanging mass was only changed. Given the angular accelerations, we conclude that when the hanging mass is increased so is the angular acceleration. Based on the observations we also see that as the hanging mass was doubled, the angular acceleration doubled as well. The same thing happened when the hanging mass was tripled, the angular acceleration tripled as well. 

 Torque Pulley

When we look at experiments 1 and 4 (where experiment uses the small pulley and experiment 4 uses the large pulley) we find that the size of the torque pulley was only changed. Based on the experiment, the angular acceleration was increased as the size of the torque pulley was increased. When comparing the size of the torque pulleys, we found that the size was doubled, as well as the angular acceleration. 

Disks Mass

When we look at experiments 5 and 6, where only the mass of the disks is changed, we find that as the mass increased the angular acceleration decreased - unlike with increasing the hanging mass and the torque pulley.

Summary

In this lab, we experimented to see how the angular acceleration would be affected by changing the hanging mass, the size of the torque pulley, and the mass of the disks. We found that each factor has a different affect on the angular acceleration of the system.

Linear and Angular Momentum