11/18/2014 Angular Momentum

Purpose:

The purpose of this lab was to learn angular momentum with an our expierment by first breaking our problem down to three steps and predicting the final height of our experiement.

Experiment:

The first part of experiment was setting up the equipment which included a meter stick, a clay ball, a stand to hold the meter stick which is spun on, and another stand to hold the clay ball.

The purpose of the device is raid the meter stick to a 90 degree angle and let the meter strick rotate at the other end of the stick which would allow the bottom end to collide with the clay ball.

L = 1m
clay = 37g
stick = 136 g

The first part of the experiment is conservation of angular energy.

Here is the formula for part 1:
mgh/2 = 1/2 I w^2

mgL/2 = 1/2(1/3ML^2)w^2

w = 5.422 rad/s

Once the meter stick collides with the clay ball energy is not coserved so we must use angular momentum which is conserved to figure out how fast the meter stick and the clay ball will be travling in an angular motion.

Here is the formula for part 2:
Iw = Iw
1/3(ML^2)w = (1/3ML^2 + mL^2)wf

wf = 2.9854 rad/s

After the colision we can once again use conservation of angular energy to predict how high the stick and clay ball will travel back up.

Here is the formula for part 2:
1/2(Iw^2) = Mgh/2 + mgh

1/2(1/3ML^2 + mL^2) w^2 = MgL/2 + mgh

h = 0.35527 m


Are actual height is very close to our calculated height. We had no sensors to measure the actual height, so we had to visually measure where the clay stopped.

Here is a picture of the setup described.

11/06/2014 Moment Of Inertia

Purpose:

The purpose of this lab is to find a spinning disk moment of inertia and measure the deceleration of the disk due to friction to predict the time for a cart attached to the disk with a wire to travel down a slope of some angle.

Experiment:

Part 1:

The first objective of the lab is to come up with a formula for the the angular acceleration of the spinning disk with friction which is as follows:

Tr - Tfriction = Ia

(Torque with respect to radius - torque of friction = inertia * angular acceleration)

We than measured the diameter of the outer and inner part of our disk.

We have the mass of the device which is labeled on the disk.

Next we calculated the inertia of the disk by adding the two types of cylinder which make up the disk we are using.

Here is the calculation from part 1:

Part 2:

Then we created the predicted formula for the acceleration of the cart which will travel down the slope.

Now we used logger pro and a camera to record the declaration of the spinning disk by it self by attaching a peace of tape on the edge of the disk and measure the time for the first revolution compared to the fourth revolution to determine the declaration due to friction.

Here is the camera we used to measure the rotations with logger pro:

Then with all the information gather we where able to predict the time it would take for the cart of 500g attached to the spinning disk to travel down the known distance which we measured with a known angle which we measured.

Here is our calculation from part 2:

Here is our experiment setup of the cart attached to the disk with the ramp:

Our predicted time was 9.2 second and our actual time measured with a stop watch was 9.73 seconds.

9/30/2014 Angular Acceleration: Part 1

Purpose:

The purpose of this lab was to measure and collect data for angular acceleration  to later find the moment of inertia, but we only seeing what factors affect the angular acceleration.

Experiment:

The experiment we used an apparatus which has two rotating disks which have a number of ticks along the side which can be used to measure the angular velocity of the disks. This apparatus also has a air hose which force air in between the two disks to create an almost frictionless surface. We used another smaller attachment on top of the disk to attack a wire which will wrap the wire will wrap around and which leads over a pulley off the table attached to a hanging mass as shown in the picture below.

We measure the diameter and mass of the top steel disk, the diameter and mass of the bottom steel disk, the diameter and mass of the top aluminum disk, the diameter and mass of the smaller torque pulley, the diameter and mass of the larger torque pulley, and the mass of the hanging mass supplied the the apparatus.

Bottom Steel:

mass = 1348 g

diameter = ?

Top Steel:

mass = 1358 g

diameter = ?

Aluminum:

mass = 465 g

diameter = ?

With our now measure values we rand six experiments to find separate angular acceleration. We used the marks of the disk which was 200 for one revolution and Logger Pro with a sensor to measure the up and down acceleration and find an average acceleration.  Experiments 1,2 and 3 are of changing the hanging mass, experiments 1 and 4 show the effect of changing radius, and experiments 4,5 and 6 show the effect of the changing the rotating mass.

Here is one example of the data we collected showing the downward and upward angular acceleration:

Here is all the data we collected: