Lab: Moment of Inertia - Find Torques & Slope for Masses 50-110g

[wolfraMshadeS]

Homework Statement

Mass m will be varied between 50-110 grams, in 20 gram increments.

Homework Equations

I need to find the torques of each run (50, 70, 90, then 110 grams). I already have the electronically-collected data for the linear accelerations of the masses:

run 1: .050 kg, .1558 m/s/s
run 2: .070 kg, .2152 m/s/s
run 3: .090 kg, .2766 m/s/s
run 4: 1.10 kg, .3480 m/s/s

The Attempt at a Solution

I've been given a hint more or less. "Note: the tension in the string must first be determined from the acceleration data, then used to calculaate the torque on the system, given that the pulley on the rotary motion sensor has a radius of 15 mm."

Here's my attempt for the first one:

mg-T=ma
.050(9.8)-T=.050(.1558)
T=0.482
$\tau$=Fr
$\tau$=Tr
$\tau$=0.482(.015)=.00723 Nm

a=r$\alpha$
$\alpha$=a/r
$\alpha$=.1558/.015=10.39 rad/s²

Then I'm supposed to plot all four sets of data as points on a graph, calculate the slope, and thus find the moment of inertia of the disk and ring combination, since $\tau$=I$\alpha$

Is this the right way to go about it?

 

[mark726]

it is important to carefully consider the data and equations provided in order to accurately solve the problem at hand. In this case, you are correct in using the given data to determine the tension in the string and subsequently calculate the torque on the system. However, it is important to also take into account the radius of the pulley in your calculations, as it will affect the value of the torque.

Your approach of using the equation \tau=Fr and \tau=Tr is correct, but make sure to use the correct value for the radius (15 mm). Additionally, when calculating the moment of inertia, it is important to use the correct units for the values of torque and angular acceleration (Nm and rad/s^2, respectively).

Overall, it seems like you have a good understanding of the problem and are on the right track. Just make sure to carefully check your calculations and units to ensure accuracy. Good luck with your experiment!