ROTATIONAL MECHANICS AP Physics 1 Exploratory Lab

Transcription

1 ROTATIONAL MECHANICS AP Physics 1 Exploratory Lab Name: Period: Date: Weight 1 (summative) DIRECTIONS: Do the activities below in groups of two or three and fill the blacks provided. STATION 1: ROTATIONAL INERTIA PART 1. Find two shapes that roll down the incline plane at approximately the same speed. 1. Using measuring devices and the following chart, calculate the moment of inertia, I (rotational inertia) of the two shapes you are experimenting with. I, Shape X: kg m 2 I, Shape, Y: kg m 2 2. Does having a higher moment of inertia, I (more rotational inertia) make the shape go down the inclined plane slower or faster? slower faster 3. What affects the moment of inertia, I (rotational inertia) more, the mass or the distance the mass is from the axis of rotation? mass (m) distance of mass (r) 4. How do the formulas for moment of inertia, I (rotational inertia) that you used above reveal which variable has more effect the mass or the radius? 5. When does a top loading washing machine have more rotational inertia? wash cycle spin cycle (at the end) hard to tell Why? Justify your answer. 1

2 PART 2. There is an adjustable hollow ring that has two sliding masses in it. 6. Where should the masses be situated to decrease the time for the ring to go down the ramp? close to the middle close to the outer edge 7. Why is this the case? 8. Draw where you would place the masses to get an irregular or lopsided roll down the ramp. d STATION 2: ANGULAR MOMENTUM 1. Have your partner start you spinning with your arms extended. Have him/her count how many times you spin in a period of time, say 5 to 10 seconds. 2. Stand on the rotating platform. Have your partner start you spinning but with your arms tight around your body. Have him/her count how many times you spin in a period of time, say 5 to 10 seconds. 3. Convert your number of rotations to radians: Arms extended Arms close to your body 4. What was your angular velocity with your arms extended? rad/s 5. What was your angular velocity with your arms close to your body? rad/s 6. What is the ratio of your angular velocities? : The angular momentum of an object is given by the formula: L = I, where L is angular momentum, I is rotational inertia in kg m 2, is in rad/s and according to the Law of Conservation of Angular Momentum, must be conserved, whether or not your arms are close to your body or extended. 7. Extend your arms. Measure the distance d from fingertip to fingertip (see Figure at above right): m 8. Now stand with your arms down by your sides. Measure the distance from shoulder to shoulder m 9. From the chart on the previous page, find the formula for the moment of inertia that best corresponds to: your shape in the arms-extended position. Write it here: your shape in the arms-retracted position. Write it here: 2

3 10. Find the ratio of the rotational inertias in the arms-extended and arms-retracted positions. Use the measurements you obtained in Steps 6 and 7 for L/r. Assume your mass has not changed in either position, so don t bother to include it. : 11. In ideal conditions, the inverse of the ratio of the rotational inertias you found in Step 9 should be the same as the ratio of the angular velocities you found in Step 5. Give two reasons for differences in the two values that may have arisen: How many spins can you do in a minute without falling off (standing up)? Call me to compete for the record and get checked off: INITIALS STATION 3: ROTATIONAL KINETIC ENERGY VS. TRANSLATIONAL KINETIC ENERGY 1. PREDICT: MUTLIPLE CHOICE. If you dropped two identical rolls of toilet paper (assuming there is no friction to speak of) from the same height, allowing one of them to fall freely while holding one end of the other one and letting it unroll, which would hit the ground first? a. The free falling one b. The one unrolling c. They would hit the ground at the same time 2. Try the experiment. Was your prediction right? YES NO 3. Find out from what height you need to drop them both so that they will hit the ground at the same time. Record your values here (also find the inner & outer radii of the toilet paper roll and record): Free-falling roll Unrolling roll Release Height (in m) Inner radius (in m) Outer radius (in m) 4. What is the initial form of energy of both rolls of toilet paper? TKE GPE CPE EPE RKE 5. What is the final form(s) of energy for the freely falling toilet paper? Mark all that apply. TKE GPE CPE EPE RKE 6. What is the final form(s) of energy for the unrolling toilet paper? Mark all that apply. TKE GPE CPE EPE RKE 7. Will mass affect the final velocity of either roll before hitting the ground? YES NO Explain. 3

4 The height ratios of the free falling vs. unrolled toilet papers is given by: Where H is the drop height of the free-falling roll, h is the drop height of the unrolling roll, r and R are the inner and outer radii of the unrolling roll. What is the theoretical ratio of the heights H (using the formula): h What is the experimental ratio of the heights H (find from your table above): h Calculate the experimental error between the ratio of the heights (you found through experimentation) and the theoretical heights (you found from the formula) % error = Theoretical value Experimental Value Theoretical Value x 100% = STATION 4: ROTATIONAL INERTIA Spin the two PVC pipes hanging from the ceiling with the same amount of force. They both have the same mass. What is different about the amount of force you need to spin them? Explain why this happens. STATION 5: ROTATIONAL INERTIA 2 Try balancing the baseball bat on one finger from one end and then flip it upside down and try to balance it from the other end. Which end is it harder to balance from? Heavier end down Lighter end down Is the center of gravity of the bat over the base (your finger) in both cases? YES NO Why is it harder to balance the baseball bat in one orientation? 4

5 STATION 6: PRECESSION PART A. Hold the bicycle wheel from its axles in a vertical position and stand on the rotating platform. Have your partner spin the bicycle wheel very fast. Now try turning the bicycle wheel 90. What happens to you? Why does this happen? PART B. Hold the bicycle wheel that is attached to the stand by a rope tied to its axle vertically (see illustration at right). Spin the wheel really fast while holding the axle horizontally. Let go of the wheel and axle. What happens to the wheel that is odd? Why does this happen? _ You are mountain biking off road. You are about to encounter a pretty rough patch of terrain. You are challenged to get over it without falling over. If you trust in the laws of physics and believe you have decent enough mountain-biking skills, why should you go over the rough terrain faster (rather than slower) to ensure that you don t fall off to either side? STATION 7: GYROSCOPIC MOTION 1. Spin the gyroscope. How long can you keep it spinning? s 2. Compete for the record (get my initials): (5 bonus points) 3. Why doesn t the gyroscope fall over? How is it able to stay balanced on such a small base?. 4. What does the balance attained by a spinning gyroscope have to do with a. the rifling of a barrel of a gun (look this up if you don t know what it is)? 5

6 b. the spinning of a football by a quarterback as s/he throws it? STATION 8: CENTRIPETAL VS. CENTRIFUGAL FORCE 1. Put a candle on a turntable shielded by an aluminium foil windbreaker the candle must be shorter than the height of the windbreaker. Light the candle and rotate the turntable. Watch the flame! 2. MULTIPLE CHOICE: Which way does the flame point? a. backwards b. to the center c. outwards d. it stays still 3. What is the direction of the flame showing? 4. Why does this happen? STATION 9: CENTRIPETAL VS. CENTRIFUGAL FORCE 2 WARNING: GET AWAY FROM ALL ELECTRONIC DEVICES AND OUTLETS FOR THIS ACTIVITY: Can you fill the bucket/container with water halfway full and spin it in a vertical circle four times without the water spilling out? Call me (better yet, film it) to show me and get checked off: INITIALS How does this simple demo show how satellites stay up in orbit around the earth? In other words, will a satellite remain in orbit at just any speed? 6

7 STATION 10: CENTRIPETAL VS. CENTRIFUGAL FORCE 3 Spin a cup of water in a vertical circle on the plate suspended by strings without spilling it (as seen in the video) Call me (better yet, film it) to show me and get checked off: INITIALS Why doesn t the water spill? STATION 11: HAMMER THROW With a partner, go out to the field where we do fire drills. Get far away from the cars. Lay out the measuring tape on the ground. Spin the hammer and throw it away from the parking lot and make sure your partner is safely out of the way. With the tape measure measure how far away you threw it. Additionally, measure the length of the rope and the mass of the hammer. Record your info here for a future calculation: Throwing distance (in m) Length of string (in m) Mass of hammer (in kg) 7