- Filtre optionnel - |
- Filtre optionnel - |
At the university, the dean and physics professor Sílvio Santos decided to implement the “roulette” evaluation method. Instead of taking written tests, students will have to spin a roulette wheel to get their grades in the subjects. This roulette wheel consists of a homogeneous disk of radius 100 cm that can rotate around a horizontal axis that passes through its center. The roulette wheel is divided into 10 equal parts, each corresponding to a grade that goes from 1 to 10, in ascending order, as shown in the figure below (no one gets a zero grade at UBF). To get their grade, students must spin the wheel and wait for it to stop. The grade that is next to the marker (arrow on the left) when the roulette stops will be the student's grade in the subject. The initial position of the roulette always corresponds to the note 10 (ten) being next to the marker, as in the figure, and the roulette only rotates counterclockwise. Consider that you requested a transfer to UBF and went there to spin the wheel to try to pass in physics. You give the roulette an initial impulse so that it acquires an initial angular velocity ω0. The roulette wheel spins, making 8 turns and still advancing to note 5 where it then comes to a complete stop. Roulette starts and always stops right in the middle of each of the divisions. Assume that a constant clockwise angular acceleration α acts from the beginning of the movement until the roulette comes to a complete stop. The time the roulette was spinning was 216.3 seconds. 1. Under these conditions, calculate the angular velocity ω0 that you gave to the roulette at the beginning of the movement. 2. Now calculate the magnitude of the constant angular acceleration α that acts during the entire motion. 3. Calculate how long it took the roulette to turn the initial half of the total angular displacement. 4. Consider a point on the wheel that is halfway between the center and the edge. Calculate the value of the linear velocity of this point, for the instant of time 25 seconds after the start of the movement. 5. Consider a point on the wheel that is halfway between the center and the edge. Calculate the value of the linear acceleration resulting from this point, for the instant of time 25 seconds after the start of the motion. 6. One of the ways you rolled a 10 would be if you made the roulette wheel spin exactly 12 full turns. Calculate what value of initial angular velocity you should have given to the roulette wheel so that it stops after completing 12 turns. Use the same angular acceleration calculated in item 2 as it is the same roulette wheel. |
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