Lab 5 Rotational Dynamics Template PDF

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Lab 5 Mandatory...

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Lab 5: Rotational Dynamics Date: 11/12/2019 Lab Section / TA Name: Rui Zou Names: Record Keeper:

Anna Greene

Group Member:

Jesse Santana

Group Member:

Xavier Valencia

Brainstorming: What limiting cases did you come up with for possible moments of inertia for the water in your can? What behavior do they represent, and what range of values might you find for each? A limiting case is that the water rotates with the can and the mass is added to the can’s in a uniform way, such that, when we calculate the inertia the water and can’s is one in the same. Simply put the water and can move together and together make a single uniform inertia as if the water is apart of the can. Another limiting case is where the can rotates independently from the water as the water would add no inertia to the can. A way to imagine this is if the water remained totally stagnant in the same position and the can’s inner walls moved completely around it with no friction and movement from the water.

Data Interpretation: Attach a plot from the software. From this, correlate the trends you observe in the displacement, velocity, and acceleration with the physical motion of the platform. Similar correlations between distance, velocity and acceleration plots these graphs all work together to demonstrate how the physical motion of the platforms work together in trends. Looking from displacement (the angle in radians through which a point revolves around a centre or line has been rotated in a specified sense about a specified axis) relates to angular velocity in where the blue highlighted area is constantly accelerating, also observed in the acceleration plot through the plateau and the eventual decline, shown in the peak and lowering of velocity. As the slope for displacement increases the velocity begins to peak, and as the displacement slope begins to slow down the velocity curve is shown to decrease and hit zero only to repeat again as it demonstrates the falling or lowering of the clip on the string.

Calibration: What object (a ring or cylinder) did you choose to measure the moment of inertia for? What was your procedure? How did you account for friction? Include any needed pictures, drawings or, sentences needed describe your setup. We measured the moment of inertia of a hollow cylinder with a mass of 500g and a radius of 3.6cm. According to the given equation of I = MR^2, we expected the moment of inertia of just the cylinder to be 0.000648 kg*m2. We only needed to measure the mass of the clip and the radius of the spool once, because they would remain the same for every trial. The clip weight had a mass of 7.8g, and the disk had a radius of 2.7cm. Once we had those measurements, we measured the moment of inertia of the apparatus without the cylinder by finding the acceleration when we dropped the clip, which was given by the software as 1.823. We then repeated the process with the cylinder on top of the disk, for which the software measured an acceleration of 1.176. We used the equation I = (mgr)/a to find the moments of inertia of the entire system both with and without the cylinder, then found the difference of those two values to determine that the moment of inertia of just the cylinder itself was 0.0006229kg*m^2, which was close to our predicted value.

Data & Analysis:

What measurements did you take in order to find the moment of inertia for water in your can? How did you combine these measurements to calculate the moment of inertia? Include any needed equations, drawings, etc. needed to describe your setup.

The measurements taken were the radius of the spool, the mass of the disk, and the angular acceleration, ɑ . Mass and radius are used to find torque. Torque can be divided by angular acceleration to solve for moment of inertia by I= using

τ (mgr) = . Uncertainty was calculated by α α

∆I =√❑ , and multiplying that by the calculated inertia. I

α

( rad/s2)

Idisk

1.823 ± 0.05665

Iw/ water

1.176 ± 0.05224

Iw/ sand

1.551 ± 0.05140

Iw/ empty

1.717 ± 0.01888

Inertia Iempty

(6.9893x10-5) ± 5.0 × 10-5

Iwater

(4.2029x10-5)

Isand

± 5.1 × 10-5

(1.2865x10-4) ± 6.6 × 10-5

Conclusions: What was the moment of inertia for the water in your can? Did it match any of your models, or is something else needed to explain its behavior? (Remember… you need

to convince the reader that you’ve done trustworthy work. Don’t just report a value. Explain the reasoning behind your choices and calculations and why this is the best measurement you were able to make.) Iwater = 0.0000420292091 kg m2. To calculate the Inertia of just the water in the can we first took the inertia of just the can (0.001202027kg m2) and the inertia of the water and the can (0.0012440506kg m2) and subtracted to get the inertia of just the water. It aligns with our models, we predicted that the water was going to slightly add to the inertia of the can but not a substantial amount. Water creates friction with the can and does not move totally independent of the can and comes into contact with the inner walls of the can contribute to the inertia, however, water’s properties don’t add a significant amount of inertia. We can compare this and validate the explanation when looking at sand’s movement with the can and how it contributes to inertia. The Isand was calculated to be 0.000128650209 kg m2, significantly higher than water’s inertia. This can be explained that sand when turning rotates with the can and adds to the inertia.

Preparation for Next Week: Next week, you will be revisiting one of your previous labs to try to resolve some unanswered questions you have, or to try and improve your experimental results. List at least two things that you might want to try, and briefly justify why. Note that you are not committed to what you list here next week; this is just to get you thinking. For the tissue rupture lab I think it would interesting to work with different ways to hold the tissue and how tension of the tissue paper affects the energy needed to rupture the tissue. I’m not sure how but being able to measure how tense the fabric is and making trials of varying degrees of tautness affects the energy needed to rupture the paper. Another question would be how the shape of the holder also affects the energy needed to rupture the paper, whether a larger circle shape or a smaller circle shape would result in different energy to rupture the tissue. OR would adding two layers of tissue paper mean two times the energy needed....