5. LOADED HOOP “Fasten a small weight to the inside of a hoop and set the hoop in motion by giving it an initial push. Investigate the hoop’s motion.”

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Presentation transcript:

5. LOADED HOOP “Fasten a small weight to the inside of a hoop and set the hoop in motion by giving it an initial push. Investigate the hoop’s motion.” 1

Example of motion - video 2

3

Outline Experimental approach Hoop properties Giving initial push Parameters Theoretical modeling Kinematics and dynamics Modes of motion Comparison of experimental data and theory Modes of motion Dependence of angular frequency on angle for different weight mass Hop analysis Energy analysis 4

Hoop properties 5 29,5 cm 99 mm 124 mm

Hoop properties Hoop 1Hoop 2 MaterialStryofoamWood ShapeToroidalFull ring Determing moment of inertia Determing distance from center of the mass Eksperimentaly -hoop was stabilised on screwdriver 6

Experimental aproach Giving initial push  Incline  Colision Method of motion recording  3 small areas marked with reflective stickers  Motion recorded in 120 fps  Stickers tracked in program for video analysis ImageJ Frame for centering and releasing the hoop 7

Theoretical modeling F N Mg weight R r ∆R 8

Modes of motion RollingRolling with slippingHop 9

Rolling 10

Rolling with slipping 11

Hop 12

Determing hoop motion Hop

Determing hoop motion

Hop analysis

16 Analysis of motion without hop - 3

17

Conservation of energy 18

Dependence of angular velocity on angle for different weight mass 19 m [g] 43, ,

Conclusion 20

Reference M. F. Maritz, W.F.D. Theron; Experimental verification of the motion of a loaded hoop; 2012 American journal of physics M. F. Maritz, W.F.D. Theron; The amazing variety of motions of a loaded hoop; Mathematical and Computer Modelling 47 (2008) Lisandro A. Raviola, O. Zarate, E. E. Rodriguez; Modeling and experimentation with asymmetric rigid bodies: a variation on disks and inclines; March 31, 2014 W. F. D. Theron, Analysis of the Rolling Motion of Loaded Hoops, dissertation, March

THANK YOU IYPT 2014 CROATIAN TEAM Reporter: Domagoj Pluščec 22

Hoop1 nM[g]k 117,842,24,330,3370,6574,92 226,250,65,170,4140,6544,01 335,559,96,10,4740,6523, ,46,950,5150,653,2 23

Determing hoops motion – another example 24

Rotational velocity in time – another example 25

26 Energy – another example