May-13-2015 Lab17: Moment of Inertia and Frictional Torque

Lab 17

Purpose of this lab is to find the moment of inertia and frictional torque on a spinning metal disk.

To do this lab:

Appropriate:

Set up equipment like the picture shown.

First: 

Determine the rotating part of apparatus's moment of inertia.
Because the rotating part has three parts. Two same cylinders and one disk.

So to find the moment of inertia of total is measure the radius of them and weight of them and add each moment of inertia together.

it's easy to find the total mass of the rotating parts, so using this to find the weight of each part.

 

Those are the data after calculation.

Radius of the disk and cylinders, mass of disk and cylinders.

On the right is how to calculate the Moment of inertia total. (Knowing the moment of inertia of cylinder and disk are 1/2 * m * r^2 if they rotate like this lab.)

Second:

Determine it's angular deceleration as it slows down, and calculate the frictional torque acting on the apparatus. 

(Because it has friction when rotating, so the deceleration acceleration is caused by friction)

To find the angular deceleration of the disk is to rotate it and using the video capture to get the velocity of a specific point on the disk. then find the acceleration, then find the angular acceleration.

Using the video capture to video the whole process of the disk slow down.

Make sure mark an obvious sign so it's easy to track where the mark went.

Follow the mark and point the mark position.

Set the Center of mass of this disk is the origin.

The disk radius as  measurement  which is 0.10025 meter

This is how the graph looks like. 

Red is the position on X axis

and  Velocity on x axis can be found.

Blue is the position on Y axis.

and  Velocity on y axis can be found.

To find the angular deceleration, set up a new column called Velocity total (Vt) which is (Vx^2 + Vy^2)^0.5

Then show the graph Vt vs time graph and linear fit a line and get the angular deceleration.

the slope of the line is the deceleration which is - 0.05329 m/s^2.

Using the formula a = alph * r
get the angular deceleration is -0.533rad /s

the torque is the
T = I * alph
T= -0.01063 N *m

Third:

Checking our data in previous.

Connecting the apparatus to a 500 -gram's cart, let the cart roll down an inclined track with some angle for distance 1 meter. Calculate how long it take  to move 1 meter from the rest.

Doing this is to compare the time by clock with the time by calculating.

Which can be find from clock.

After three experiments which are let the cart go distance 1 meter and record the time and get the average time which is 7.2 second.

To check the data should to derive a equation compare the time on experiment value and the real time measure by clock.

Draw a force graph, and analyse the force.

Three equations, Know that angle which is 48 degree measured, m is 499 grams, Torque friction is 0.01063 N* m, I-total =0.02 kg*m^2, radius of the small disk is 0.01575 m. Three unknown are T, angular acceleration, and acceleration. 

Plug and change the three functions and replace the T and angular acceleration and into one function and input the data.

Obtained acceleration a = 0.0366 m/s^2

Using the newton laws and with constant acceleration.


plug the data d= 1 m, a = 0.0366 m/s^2


get the t = 7.4 s.

Uncertainty of time off by 2.7 %.

Conclusion

 The lab is about fining moment of inertia and frictional Torque, and using those data with another experiment to test and check the results which are acceptable.

Uncertainty sources:

1.The Graph of velocity vs time
2. The timer when reading and recording the time.
3. Mistakes made by people during experiments.