# Bicycle wheel and swivel chair

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1 Aim: To show conservtion of ngulr momentum. To clrify the vector chrcteristics of ngulr momentum. (In this demonstrtion especilly the direction of ngulr momentum is importnt.) Subjects: Digrm: 1Q40 (Conservtion of Angulr Momentum) Equipment: Swivel-. Bicycle wheel with hndles nd leded rim. Sfety: When hndling the bicycle wheel for the first time, prctice with it stnding firmly on the ground nd not on the swivel-, becuse the direction of the experienced forces might tke you by surprise nd hurt you. When you wnt to stop the bicycle wheel, slowing it down to stop with your hnd, be creful not to burn your hnd.

2 Presenttion: 1. The demonstrtor sits on the swivel- nd holds the bicycle wheel in front of him. The wheel is held with its xis verticl. The demonstrtor spins the wheel nd immeditely he strts rotting in the opposite sense. When by hnd he stops the wheel, lso the swivel stops. 2. The demonstrtor sits on the swivel. An ssistnt hnds him the bicycle wheel tht is spinning lredy round the verticl xis. Before doing so, sk the udience wht will hppen? Answer: nothing! But when the demonstrtor slows down the bicycle wheel by brking it, the swivel- with demonstrtor will strt turning round in the sme direction s the bicycle wheel did. 3. The demonstrtor sits on the swivel. An ssistnt hnds him the bicycle wheel tht is spinning lredy round the horizontl xis. Agin nothing hppens. But if he then turns the spinning wheel to verticl position of its xis, he will rotte in the opposite sense to the spin of the wheel. Turning the wheel nother 90º, so the xis is horizontl gin, it brings him bck to stop. Turning the wheel nother 90º mkes him turn gin but now in opposite direction. When the demonstrtor continuously turns the xis of the spinning wheel, then the swivel- will turn in one sense nd then to the other nd so on. 4. Agin the ssistnt hnds spinning bicycle wheel to the demonstrtor tht sits on the swivel (wheel xis verticl gin). When the demonstrtor on the swivel- turns the xis 90º then the demonstrtor strts turning. When he turns it nother 90º then he rottes even fster! (2x) 5. When there is time to prctise with your ssistnt, you cn continue this demonstrtion in the following wy: Strt in the sme wy. (The demonstrtor sits on the swivel ; the ssistnt hnds over the turning bicycle wheel - xis verticl -; the demonstrtor turns it 180º.) Now the demonstrtor, while rotting on the swivel-, hnds the wheel bck to his ssistnt, who in turn rottes the xis through 180º nd gin hnds it to the demonstrtor on the swivel. When the demonstrtor now turns the spinning wheel over second time, his ngulr velocity increses (doubles). Additionl "qunt" my be given to him by repeting this process. If, however, the ssistnt fils to turn the wheel over once but turns it over ech time therefter, the process becomes subtrctive.

3 Explntion: 1. Mking the wheel turn, it obtins n ngulr velocity nd n ngulr momentum L=I. Figure 1 Then the swivel hs to turn in the opposite sense with n ngulr velocity ', whose ngulr momentum equls -I (see Figure 1b), becuse the totl ngulr momentum of the system hs to remin zero s it is in the beginning of the demonstrtion (Figure 1). 2. The wheel hs n ngulr momentum of L=I (see Figure 2). This ngulr momentum is conserved, so when the wheel stops, the swivel with demonstrtor will strt to rotte (see ' in Figure 2b) in the sme direction s. b Figure 2

4 3. When the rotting wheel hs its xis in horizontl position (Figure 3), then there is no ngulr momentum in the verticl direction. The swivel is not rotting. Turning the wheel 90º upwrds (Figure 3b), then n ngulr momentum is introduced in the verticl direction (I. This hs to be compensted by nother ngulr momentum of the sme mount (-I in order to keep the totl ngulr momentum in the verticl direction zero: the swivel nd demonstrtor will rotte ( ' in Figure 3b). Bringing the wheel down (see Figure 3c) will mke the swivel turn into the other direction. (The disppernce of I in the horizontl direction hs no rotting effect, becuse the set up cnnot rotte round horizontl xis. The only effect is torque felt by the demonstrtor.) c Figure 3 4. In the beginning the wheel is turning, so there is n mount of ngulr momentum: L=I nd the swivel is stnding still (see Figure 4). Bringing the rotting wheel to horizontl position removes tht ngulr momentum from the system, but since ngulr momentum needs to be conserved, the whole system strts rotting ( ' ) in the sme direction s When the wheel is lowered once more (Figure 4c), the figure mkes cler tht the swivel hs to speed op to 2

5 b c Figure 4 5. This is repeting the procedure of sitution 4 number of times. In the beginning the swivel is not rotting. At the end of the first round it rottes with 2 Then fter the second run it rottes with 4 fter the third run with 6 nd so on. Remrks: After the demonstrtion we hve more bicycle wheels nd swivel s in our lecture hll so the students cn prctice themselves nd experience those strnge forces/torques. Sources: Borghouts, A.N., Inleiding in de Mechnic, pg. 173, 174. Sutton, Richrd Mnliffe, Demonstrtion experiments in Physics, pg. 75, 76. Leybold Didctic GmbH, Gerätekrte, Mnsfield, M nd O'Sullivn, C., Understnding physics, pg. 105.

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