Lab 18: Lab Problem – Moment of inertia and frictional
torque
Authors: Mohammed Karim, Bemaya, and Louis.
Objective: Find the frictional torque done by the wheel and
determine the time it would take for a car tied to the wheel to slide down the
track.
Theory/Intro: We understand that inertia acts as a system
and, as a result, can ratio the values to find the mass and inertias of each
individual object.
Apparatus/Procedure:
In this
lab, we are given a metal disk that spins on a shaft and are tasked with making
measurements of each of the parts. We then calculated the volume of each
individual “cylinder” and used proportions to find the mass of the disk and the
supports. (See Figure 18.1) Then, we recorded the spinning and marked it using
LoggerPro to find the deceleration. This value, the angular deceleration due to
friction, was 0.5551 rad/s^2. We then calculated the torque due to friction (See
Figure 18.2) Now that we had the frictional values, we could run the car down
the 1 meter track. We set up a sum of force equation and concluded that the car
would have an acceleration of 0.0333 meters/second^2. Finally, by using
kinematics, our theoretical time for the time it would take the car to travel 1
meter was 7.76s. (See Figure 18.3) After running the experiment, our
experimental value was a bit lower than our theoretical value, but by less than
4%.
Data Tables/Analysis:
Figure 18.1 - Calculation for the mass of the metal disk and the torque due to friction
Figure 18.2 - Value for frictional deceleration (off by a factor of 10; did not do meters)
Figure 18.3 - Calculations for the time it would take the cart to travel 1 meter
Conclusion: This lab, being a giant problem, is basically a
two part question, in which first you must find the frictional torque behind
the spinning of the wheel, then you must use it to calculate the acceleration
of the car and, as a result, the time it takes the car to travel one meter. Overall,
our theoretical value was very close to our experimental value, but could be
off due to the uncertainty of our calculations, the uncertainty behind the
ratios of mass to volume, the uncertainty behind the angle the track makes with
the horizontal, and the fact that we neglected the friction due to the track
and the car. However, if these values were considered, we would have seen a far
more precise answer.
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