Lab #17: Moment of Inertia and Frictional Torque

Purpose: To calculate the moment of inertia of a large disk and two cylynder system that spins around its central axis. We also calculated the angular decceleration due to frictional torque. Lastly we used these and other concepts to predict how long it would take for a cart to travel a certain distance when wound around the small radius of the system.


Procedure: To find the moment of inertia for the disk-cylinder system we broke down the object into pieces we could handle seperately to find each one's moment of inertia. We used symetry to split the shape into one large disk and two long cylinder of identical volume on each side of the disk. We then measured and labeled the diameter, radius and thickness of the disk and cylinders.



One issue we faced was not being able to take the object apart to measure the mass of each piece. To work around this we used the total mass(which was etched into the disk) of the object and set up equilevant equations comparing the total mass and total volume to the individual mass and volume of each shape. We then solved for the masses of the disk and cylinders seperately.



To find the moment of inertia for the system as a whole, we found the inertia for each of its parts and combined them. Because each indivisual shape was either a wide or elongated cylinder we used I=1/2*m*r^2 to calculate each individual moment of inertia.



We know this apparatus will have a frictional torque that will work against the later pull of the cart. To calculate the angular decceleration of the system we ran several runs where the wheel spun at different speeds and slowed down  due to friction reaching final velocity of zero while we measured how many rotations it completed to stop. We then averaged our trials and found a good value for the decceleration of the system.



Know that we have the values for the forces in this experiment we set up likear kinematic equations for the motion of the cart and rotational kinematics for the disk and through clever manipulation we solved for our predicted time it would take the cart to travel down the track.



Finally after all our calculations we can run the actual experiment and measure how long it takes the cart to make it down the ramp. We ran two seperate trials to collect and compare our teoretical and actual values.



Our percent error for each trial was very small and most likely caused by minor experimental errors such as friction between the cart and track or our tangential string not being perfectly parallel to the track. However, this experiment did produce very good results while still being conceptually rich.