Lady Bug Rotational Motion Lab

Lady Bug Revolution Activity Part A. Relation between angular position θ and l X, Y coordinates. 1. Click on Rotation tab. Under show graphs click θ, ω, x, y. Set angular position θ to 0 and angular velocity ω to 36 deg/sec. With this velocity the platform will rotate by 90 degrees every 2.5 seconds, which is division on the time axis. Place Ladybug at 1 m from the center (use ruler tool). Start rotation, let platform make one full revolution. Observe how θ and X,Y depend on time. Move Ladybug to 4 m and repeat one full revolution. Observe how θ and X,Y depend on time in this case. What does change with the radius of Ladybug position? (C.S) The purple line representing the position of the ladybug in the x axis and the red line presenting the position of the ladybug in the y axis are much closer and have a longer wavelength. 2. Think of relation between X,Y and θ. Pick right equation: a) For X: X = R sin θ; X= R cos θ; X = 1/R sin θ; X= 1/R cos θ; b) For Y: Y = R sin θ; Y= R cos θ; Y = 1/R sin θ; Y= 1/R cos θ; Run your simulation several times changing R to make sure you picked right equation. 3. Using these equations calculate Ladybug X,Y coordinates when it is at 1and 4 m and θ = 0, 22.5, 45, 90, 180, 270 degrees. Fill out the Table θ 0 22.5 45 90 180 270 R x y x y x y x y x y x y 0 .92 .38 .71 .71 0 1 -1 0 0 -1 1m calc 1 1 .06 .90 .44 .66 .75 -.06 1 -1 -.06 .06 -1 meas 4 0 3.7 1.53 2.83 2.83 0 4 -4 0 0 -4 4m calc 3.99 .07 3.66 1.6 2.77 2.88 -.07 3.99 -3.99 -.07 .07 -3.99 meas Now run your simulation again placing Ladybug at 1 and 4 m and measure X, Y position at the same angles. Write those numbers in the Table. DO your calculations agree with measurements? The calculations agree with the measurements. Part B. Angular and Linear Velocities, acceleration. 1. Use the internet to define angular (aka rotational) velocity. The rate at which a rotating object’s angle changes to a fixed axis. 2. Under show graphs click on θ, ω, v. Click the minimize button on the θ graph. Type 180 in for angular velocity and click “go”. This will make the turntable turn at a rate of 180 o per second. Look at the vector arrows coming from the ladybug. A) What direction is her centripetal acceleration? B) What direction is her tangential velocity?(C.S) A. it points towards the center B. the velocity is pointing tangent to the circular path the ladybug makes and direction of travel 3. Experiment with changing to location of the ladybug and beetle on the wheel. How does position relative to the center of the wheel affect the angular velocity? (C.S.) The angular velocity is still pointing tangent to the circular path the ladybug makes and direction of travel no matter where the ladybug and beetle are placed. 4. Click on the ruler box at the bottom left of the screen. A) How long is the ruler? (Always include units!) B) How wide is each band of color on the turntable? A. 8 meters. B. Gray center is 2 meters, light blue second inner circle is 4m, green circle is 6m and the outer circle is 8m. 5. Place the ladybug at 1m distance from the axis (center) of the turntable. A) Record the ladybug’s tangential velocity as V L . (This is simply referred to as velocity on this simulation, and it is written in green on the velocity graph.) Place the beetle at 2m from the axis. B) Record the beetle’s tangential velocity as V B1 . C) Move the beetle to 3m from the axis. C) Record the beetle‘s tangential velocity as V B2 . D) Explain how the radius (distance from the axis of the turntable) affects the tangential velocity? (C.S.) A. B. C. D. V L = 3.029 m/s V B1 = 6.118 m/s V B2 = 9.494 m/s The ladybug never moved from her spot that was 1m away from the center so her tangential velocity stayed the same while the beetle’s tangential velocity doubled but was 2m away from the center. The farther the insect moves away from the axis of the turntable, the higher the tangential velocity. 6. A) Record both bugs’ tangential velocities. Double the angular velocity to 360 o /s and record the new tangential velocities. How does doubling the angular velocity affect the velocity of the bugs? (C.S.) A. When the angular velocity is 360 o /s, the tangential velocity of the ladybug is 6.057 m/s and she is still 1m away from the center, the tangential velocity of the beetle is 18.989 m/s and is 3m away. a. Doubling the angular velocity is doubling the bug’s previous velocity value. 7. Since the angular velocity is currently 360 o /s, the period T is 1 rotation/s. A) Using v = 2r/T, calculate the tangential velocity the beetle would have if you moved him to the edge of the turntable (a radius of 4 m from the axis). B) Move the beetle to r = 4 m and record his tangential velocity. A. 24.18 m/s ((2*4/2pi)18.989) B. 24.358 m/s 8. If the huge beetle has a mass of 8.0 kg, find his centripetal acceleration a the average centripetal force F c on the beetle? c . D) What is A. This is me assuming the huge beetle is 4m from the center of the turntable, has a tangential velocity of 25.031 m/s and an angular velocity of 360 degrees per second (6.28 rad/sec). a. a c = (6.28) 2 (4) = 157.75 m/s 2 b. F c = (8)(6.28) 2 (4)= 1262.03 N 9. If the ladybug has a mass of 6.0 kg and is at a distance r = 1 m, find her A) velocity, B) centripetal acceleration, and C) centripetal force. A. This is me assuming the ladybug has a tangential velocity of 6.057 m/s and an angular velocity of 360 degrees per second (6.28 rad/sec). a. v=(6.28)/1= 6.28 m/s b. a c = (6.28) 2 (1) = 39.44 m/s 2 c. F c = (6)(6.28) 2 (1)= 236.63 N