Lab 18 Moment of Inertia and Frictional Torque

Ana Leyva, Jonathan Goei
5/22/17

By doing this experiment we are trying to find the moment of inertia of the system, the frictional torque, and we are trying to use this information to find out how long it would take a car attached to the metal disk to travel a certain distance.
In order to do all of this we first have to measure our apparatus that is made up of three different cylinders. We will use this information to find the moment of inertia of the system. We will then use this information to find the frictional torque acting on the system. However in order to calculate this we first have to find out at what rate the apparatus decelerates at. We will find out the deceleration speed by recording the apparatus as it spins and then using logger pro to see at what rate it slows down. Then using a free body diagram we will calculate the acceleration of the cart as it rolls down a ramp and using this acceleration we will solve to see how long it would take the cart to roll down one meter. We will then check our calculations by doing three trial runs to see if they are close to our theoretical time.

Our Lab set up

The first thing we did to start off this experiment was to measure the diameter and the height of the three connected cylinders that made up our apparatus. We then used this information to solve for the volume of the three cylinders. Which we them used to solve for the mass of those three cylinders. Finally we found the moment of inertia of each of the cylinders and added them up to solve for the total moment of inertia. Then using this information and the free body diagram that we drew we solve for the frictional torque which in turn helped us find a relationship between the apparatus and the acceleration of the attached cart. Finally we used this acceleration to calculate how long it would take the cart to travel one meter down a slope. To confirm our calculated time to travel 1 meter down a slope we then did three trial runs whose time was really close to our calculated time.

Measured values

Deceleration Rate 

Solving for Volume and Mass

Moment of Inertia

Calculating Acceleration and Frictional Torque

Solving for time for the cart to travel 1 meter

As you can observe from the last picture the trial time were extremely close to our predicted time. The reason why they are not perfect can be due to human error in starting and stopping the stopwatch. I believe that this is the main reason why our times aren't exact but other things that might be slowing down our cart could be air resistance and unaccounted friction of the cart going down the ramp.