22-May-2017: Momentum of Inertia and Fictional Torque

In the past, we have already verified that the calculate inertia meets with the actual inertia. In theorem, because at any moment, rotational friction is always static friction, which implies that it should not consume any energy. However, from small marble to car, we know that it still consume some energy. Today, we did a lab on a rotational disk to study the rotational friction (or frictional torque).

Purpose

Find out the frictional torque of a spinning disk.

Plan

First, calculate the disk's momentum of inertia by its shape and mass.

Then, capture a video that the disk is rotating and decelerating.
Use the Logger Pro to find out the acceleration of the disk.
By the function,

we could know the frictional torque. 

Then, use another model which is the same disk and pull by a car. 

Predict the time that it need to slide for a distance by functions. 

Compare it predict time and actual time to see whether the frictional torque is correct. 

Set up & Data

1. Make appropriate measurement of the rotating part of the apparatus and determine its moment of inertia. 

2. Spin the apparatus. Use video capture determine its angular deceleration as it slows down. Calculate the frictional torque acting on the apparatus. 

which says the angular acceleration is -0.4395 r/s^2

3. Connect the apparatus to a dynamics cart. Set up the apparatus as follows. The cart weights 572g. 

4. Let the cart slide down for 1 meter, and record the time. And we got 6.92 s. 

To record the most accurate time, our team (4 people) collected the time together, and we use the average of them.

Analyses 

For the inertia, we can get from the data of shape and mass. 

Then, total inertia is 0.0213858583075759 kg*m^2. 

So by the function 

we know the frictional torque is -0.00939908472617959 N*m

Solving the functions above, we can get the angular acceleration is 

in this case is 2.590426854535 r/s^2

Then by function 

We can calculate the time is 

Plug in the number, and I get 7.03504746291719s, which is only 2% off. 

Conclusion

This result comes out that the predicted value is pretty close to the actual value. And because the time is collected by people, there might be small different from actual value. Moreover, there are some uncertainty in the measurement. One thing really important is that while the cart was sliding down, there are also some frictional torque on the wheels, which is ignored. 

In general, the result confirmed what we thought, which is there is some frictional torque while the disk is spinning, and the magnitude will not change even though we apply different force. It is some kind similar to kinetic friction.