Lab #18: Moment of Inertia and Frictional Torque
Dahlia - Rafael
Dahlia - Rafael
14-Nov-2016
The purpose of the lab#18 is to determine the time an object takes when it is connected with a rotated disk by a string in a given distance. And then, compared the time it takes by experimental value and theoretical value.
I. Theory:
To calculate the time, we had to have to know the acceleration of the object. To find it, we tried to figure out the angular acceleration of the disk.
So we had:
So, the angular acceleration of the disk depended on the radius of a small pulley, the mass of the cart, the angle of track, the inertia of the disk and the angular acceleration of friction.
And finally, we could calculate the time it takes
II. Produce:
1. Inertia of the disk:
I=(1/2)*(mass of disk)*(radius of disk)^2
but the issue here was we did not know what the mass of the disk was; thus, we tried to figure out the mass of disk.
So, first, we measured dimensions of the disk-pulley.
Then, we calculated the mass of the disk.
And we came up with the mass of the disk was 4.18 kg.
Now, we could easy to calculate the inertia of the disk when it rotated around it center with mass = 4.18 kg and radius =0.1005 m
the inertia = 0.02092 kg*m^2
2. Angular acceleration of friction:
We recorded the rotated disk and put it in lab pro to figure out the angular acceleration of friction.
First, we marked a tape on the disk, then recorded every points of this tape.
Then, we pointed them in the log pro, and we get the graph of position vs. time
The log pro also provided the velocity of this tape vs. time.
So, we could have the angular velocity of this tape was velocity/radius
and the angular acceleration of friction was the slope of the graph angular velocity vs. time.
and it was 1.58 rad/s^2
Once again, I listed needed data to calculate the angular acceleration of disk.
Then, I found the time it took to travel 1 m with the angle 40 degrees.
The theoretical time was 11.276 s.
3. Experimental value:
we set up the cart connected with the rotated disk by a string. This cart traveled in the track made 40 degrees with the horizontal. Then, we used timer to get the time this cart travel 1 m.
This was what we had after 3 trials:
4. Comparing the theoretical value with the experimental value:
I entered these data to a sheet of excel and calculate the percent error.
III. Conclusion:
When Comparing to the theoretical time vs the experimental time, the percent error came out only -0.67% error, and this was a really good result.
I. Theory:
To calculate the time, we had to have to know the acceleration of the object. To find it, we tried to figure out the angular acceleration of the disk.
So we had:
And finally, we could calculate the time it takes
II. Produce:
1. Inertia of the disk:
I=(1/2)*(mass of disk)*(radius of disk)^2
but the issue here was we did not know what the mass of the disk was; thus, we tried to figure out the mass of disk.
So, first, we measured dimensions of the disk-pulley.
Then, we calculated the mass of the disk.
Now, we could easy to calculate the inertia of the disk when it rotated around it center with mass = 4.18 kg and radius =0.1005 m
the inertia = 0.02092 kg*m^2
2. Angular acceleration of friction:
We recorded the rotated disk and put it in lab pro to figure out the angular acceleration of friction.
First, we marked a tape on the disk, then recorded every points of this tape.
Then, we pointed them in the log pro, and we get the graph of position vs. time
The log pro also provided the velocity of this tape vs. time.
So, we could have the angular velocity of this tape was velocity/radius
and the angular acceleration of friction was the slope of the graph angular velocity vs. time.
and it was 1.58 rad/s^2
Once again, I listed needed data to calculate the angular acceleration of disk.
3. Experimental value:
we set up the cart connected with the rotated disk by a string. This cart traveled in the track made 40 degrees with the horizontal. Then, we used timer to get the time this cart travel 1 m.
This was what we had after 3 trials:
4. Comparing the theoretical value with the experimental value:
I entered these data to a sheet of excel and calculate the percent error.
III. Conclusion:
When Comparing to the theoretical time vs the experimental time, the percent error came out only -0.67% error, and this was a really good result.
Errors occur because of the friction between the carts wheels and the track. and the string not completely parallel with the inclined track.
From now on, if we do not have a timer, and we need to find the time the cart takes in a certain of distance, we can use the angular acceleration of the disk to know the needed time.
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