- Angular acceleration moment of inertia formula pro#
- Angular acceleration moment of inertia formula trial#
This assumption would make our predictions larger than the actual value, which is what we observe.
Our theoretical predictions assume that the pulley at the edge of the apparatus has no mass and is frictionless. Here is a datatable with the other disks moment of inertia (experimental and theoretical).Ĭonclusion: With percentage errors a little less than 10% there are a couple candidates for causes of error.
Angular acceleration moment of inertia formula trial#
The justification for this is provided below:īelow is a sample calculation for one of our theoretical moments of inertia for trial 6:īelow is a sample calculation for one of our experimental moments of inertia: This effectively cancels out the frictional torque’s affect on the angular acceleration. When we measure our acceleration we can take the average between when it is accelerating during the unspooling phase and when it is accelerating during the spooling phase. The affect of this frictional force is equal in both directions and therefore can be cancelled out. This was our data table:īackground info: It is possible to prevent the frictional force from playing a role in our calculations since it acts against the acceleration on the way down and with the acceleration on the way up. Record both acceleration values along with the corresponding values for mass of hanging mass and which objects were used. Since this data will be angular velocity vs time, we can take the slope to determine the acceleration. (note, you may have to extend the data collection length). Once the sensor starts reading data, release the hanging mass from rest and allow it to fall, causing an angular acceleration to the disks. Spool hanging mass to the edge of the table and start collecting data. Hook up known hanging mass to torque pulley of known diameter.
Angular acceleration moment of inertia formula pro#
Rotate the disk and make sure that logger pro reads that the disk has some angular velocity. In logger pro, adjust the “lines per rotation” to 200 for the rotary sensor. This is an example of what the apparatus should look like, (without the triangle) Place appropriate disks on apparatus and attach/activate air hose to reduce the friction between the disk and apparatus. Next, set up angular velocity measurement device with logger pro. These include: Mass and diameter of steel and aluminum plates, mass of hanging mass and diameter of torque pulleys. The first step is to measure all the parameters necessary to do our calculations. After calculating the experimental angular acceleration (and accounting for friction) we can compare the theoretical moment of inertia with the experimental. We can do this by measuring the applied torque, and resultant angular acceleration (both positive and negative). The second half of this lab will attempt to calculate the value for our disk’s moment of inertia. If the moment of inertia is increased -possibly through increasing the mass of the disk- we expect angular acceleration to decrease. We expect, for example, that if applied torque increases then angular acceleration increases.
If the torque being applied is doubled, how will that affect the angular acceleration? In the lab we will change one parameter at a time and observe the resulting changes. The first part of this lab will attempt to demonstrate how changing these parameters will affect angular acceleration. This parameter, along with the magnitude of torque being applied, affect the magnitude of the angular acceleration of an object in accordance to the following equation: Torque = (moment of Inertia) * (angular Acceleration). The larger an objects moment of inertia, the more difficult it is to rotate. Objects have the same property when it comes to angular acceleration, called moment of inertia. Theory: Inertia, put simply, is an objects resistance to being accelerated. To use data collected to calculate moment of inertia of our disk. Purpose: Observe the affect that changing parameters such as hanging mass and disk radius have on angular acceleration. Mirielle Sabety, Keane Wong, Anthony Moody
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