Moment of Inertia *** Purpose *** The purpose of this lab experiment is to determine the moment of inertia of a rotating solid object by several different methods and com pare the results in terms of the anticipated possible error.
*** Equipment *** Pasco timer 8025, bicycle wheel and axle, test tube clamps, stand, long rod, rod , string, tape, hanging masses, photo timers, meter stick, balance, and thumb tacks.
*** Theory *** All rotating objects have a property called rotational inertia or moment of inertia (I). The moment of inertia is dependent on its mass M and the distribution of that mass. The un it of 2 rotational inertia is (kg-m ) We can break down objects into pieces and analyze each piece mathematically.
*** Procedure *** 1. 2. 3. 4.
Measure total mass of the wheel. Break wheel down into a series of parts. Measure mass of each part and treat as proper component. Calculate the moments of inertia of each part and compare the moment of inertia of each part to the total. (Force Method)
5. Mount tire so that it is free to rotate about a horizontal axis. 6. Wheel must be level. 7. Attach a 1.20 meter long length of strength, with a loop at both ends, to the outer circumference of the tire. 8. Roll string onto the tire so that loose hoop is horizontal from the axis of rotation. 9. Hang 500g mass from this loop.
10. Attach the mass so it will drop off after one half revolution. (L= ∏r o) 11. Two markers are needed:
1 to start photo timer
1 to stop photo timer 12. Repeat process a total of 10 times. 13. Calculate linear acceleration then velocity for all 1 0 trials. 14. Do force and torque equations. 15. Solve for rotational inertia I for each.
(Energy Method) 1. Attach the mass so it will drop off after one half revolution. 16. Two markers are needed:
1 to start photo timer
1 to stop photo timer 17. Time the revolution. 18. Repeat process for a total of 10 trials. 19. Calculate the linear attached velocity at the drop for each trial. 20. Solve for I for each. 21. Count the number of turns it takes until u ntil the wheel. (Only 1 trial needed) 22. Calculate initial potential energy, kinetic energy of falling mass at en d of spin, kinetic energy of the wheel when the mass drops, and energy loss per revolution. 23. Calculate percent difference between the three method s.
*** Calculations *** 2
2
2
Axle: ½m(r ia ia + r oa oa ) 1
2
a= 2*L/ta = 2*∏*r o/ta
2
Spoke: ( /3)mr i
v= a ta 2
2
2
Wheel and Tire: ½m(r i + r o )
I= mr o (g-a)/a = mr (g/a-1)o
∆U + ∆K rot rot + ∆K trans trans = 0
v= 2∏r o/tr
2
I= m(2g∏ m(2g∏r o/v -1)r o
2
2
*** Errors *** There are many possibilities that could lead to the percent difference other than human negligence. No friction was taken into account, ac count, such as the friction of the wheel w heel against the handles, or the friction of the pulley or rope. This very well may be the th e cause for the loss of energy per revolution. Another source of e rror could be that the mass was dropped d ropped below 0 degrees or inconsistent with its angle during the ten trials. This would measure in inaccurate photogate readings as well as a lower calculated velocity. If the tire was not level and/or remained level throughout all the trials could also result in inaccurate results. How the tire was released each time could as well. If the tire was released with a little push, not equal to a little push in all the trials then the recorded data would not be precise. One more source of error could result from the rope entering the grooves of the tire. This could cause friction as well as the distance of rotation; again resulting in inaccurate data. The markers accuracy and consistency of placement could also be a factor in possible errors.
*** How does friction affect the answer? *** The time it took the marker to travel to the photo gate was used in calculating the velocity as well as the acceleration in the force method. Friction, which was not calculated calc ulated in this experiment, would result in less than accurate time readings, the velocity, and acceleration of all trials. This would then result in all other calculations to be less accurate as well.
