What is the angular acceleration of the rotating platform?

[Elkay]

Recently had a lab on Rotational motion and mass distribution (strange as it wasn’t covered in class yet), and there were a few questions I needed to answer. I’m doing my best to understand the lab and concept, and I was hoping that someone could possibly broaden my understanding and tell me if I am on the right track:

The lab consisted of an apparatus with rotating platform. Near the bottom on the spindle, there is a string that is attached to it and a hanging mass, which is here:

http://home.earthlink.net/~copper017/Class/Physics/lab/RotatingPlatform.jpg​

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I performed 3 trials with different radius sizes R on the platform (first was 0.25m, second was 0.30m, and third was 0.35m) with a hanging mass that was 2.67kg. I noticed as the platform’s radius got larger, it took more time for the mass to fall, and the acceleration (a) became smaller. However, as the radius became larger, the moment of inertia (I) became larger. So the bigger the radius, the longer it would take for a rotating object to reach its moment of inertia, right?

Here are my calculations and lab questions:
1. Does the plot of R2 versus I pass through the origin? Why? The plot does not pass through the origin. Passing through the origin would suggest that there is no moment of inertia at a given moment during rotation.

2. Could you measure the distance the mass falls by counting the number of rotations the rod makes? Would this be a better way to measure the distance? It is possible to find the distance if the radius of the spindle is known and its circumference is found. The difference of the height of the mass would be equivalent to the circumference of the spindle multiplied by the number of rotations around the spindle. Directly measuring and subtracting the initial and final height of the mass during the experiment would be a simpler way of finding the distance that the hanging mass falls.

http://home.earthlink.net/~copper017/Class/Physics/lab/table-3.jpg

http://home.earthlink.net/~copper017/Class/Physics/lab/chart-3.jpg​

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[chaoseverlasting]

Thats funny. I would imagine that it would take the mass lesser time to fall as the radius increases, cause centrifugal force is mw^2r. If w for each trial is constant, and radius increases, then so does the centrifugal force. If there is an angular acceleration, then the picture changes and you would have to bring in moment of inertia, otherwise, I don't see why that factors in.

 

[Mentz114]

Passing through the origin would suggest that there is no moment of inertia at a given moment during rotation

I think you don't understand what momemt-of-inertia means. It has nothing to do with time. The MoI of a disc, for instance, depends on its radius and mass distribution. It is the rotational equivalent of inertial mass. For a rotating object the rotational energy is 1/2 Iw^2 like kinetic energy is 1/2 mv^2.

 

[Elkay]

Thank you for the replies and corrections. I don’t quite get everything, but I am trying. :)

I think you don't understand what moment-of-inertia means. It has nothing to do with time. The MoI of a disc, depends on its radius and mass distribution. It is the rotational equivalent of inertial mass...

… Okay. So going by what you said --(not looking at time):
If I am to just focus on the radius and mass, then by making the radius of the platform larger would place the large masses (M) farther away from the center of rotation. As the majority of the mass is placed away from the center, then the resistance to an “angular acceleration” during rotation (moment of inertia) increases, correct? (BTW, I don’t completely understand “angular acceleration”- I think it has something to do with “torque,” and I don’t get that concept, either).


As for the graph, the y-intercept occurs when x=0, or in this case, when the radius squared (R^2) is 0. Since there is a positive y-intercept, the graph is suggesting that there is a resistance to change during rotation even if an object has the majority of its mass near the center of rotation. There would be a moment of inertia for an object with such a radius, however, its resistance would be much smaller than an object with its mass distributed farther away from the center.

 

[Mentz114]

...then the resistance to an “angular acceleration” during rotation (moment of inertia) increases, correct?

The graph just shows the relationship between MoI and r because

I = mR^2

See http://en.wikipedia.org/wiki/Moment_of_inertia

 

[chaoseverlasting]

Initially, the platform was at rest. Then, it started moving and in a certain time t, it gains an angular velocity w. Therefore, the angular acceleration is w/t.