4 Circular-Motion Online

P hy s i c s L a b ( O n l i n e S i m u l a t i o n ) CIRCULAR MOTION Mechanics TA name: Francisco Tabia Due Date: Student Name: Student ID: Simulation Activity #6: Ladybug Revolution Simulation created by the Physics Education Technology Project (PhET) c/o The University of Colorado at Boulder http://phet.colorado.edu/

P hy s i c s L a b ( O n l i n e S i m u l a t i o n ) Investigating Rotational Motion: Angular kinematics and relating angular to linear quantities. Objective: This activity is intended to enhance your physics education. We offer it as a virtual lab online. We think it will help you make connections between predictions and conclusions, concepts and actions, equations and actual motions. We also think that if you give this activity a chance, it will be fun! This is an opportunity to learn a great deal. Answer all questions as you follow the procedure in running the simulation. Join the ladybug and beetle in an exploration of rotational motion. It is possible to determine the angular and linear quantities which can describe the motion of a ladybug on the turning table. All features you need for this simulation can be found on the display by clicking the “Rotation” tab. Graph Type: Click one of the types of graphs among the four types under the “Show graphs”. If you couldn’t recognize the symbols, click “Symbol Key” Graph Selector: There are three boxes to check and select from. To display graphs which represent the motion of the platform (the turning table), check the “Show Platform Graph” box. Checking this box also helps you to enter values of angular quantities. The other two boxes are used to add position, velocity, and acceleration of the ladybug and/or Beetles. Position: You can place the ladybug and/or Beetle on the platform. The position can be measured using the ruler by checking the “Ruler” box. Vectors: you can check the boxes at the bottom left corner to display the vectors on the ladybug and/or Beetles. In addition, you can see the results in both radian and degrees. Whenever you are ready to run the simulation, click “Go”. You can control the speed of the simulation using “Sim speed” slide. You can always restart the platform by clicking on “Rewind” and clear the graph by clicking “Clear”.

P hy s i c s L a b ( O n l i n e S i m u l a t i o n ) 2. Click “Reset All” again and this time drag the Beetle on the turntable and put it at (3,0). Set the angular velocity of 100 degrees/s. Now click “Go” and stop it after the turntable rotates twice. Make sure you did click on  ,  ,v graph to answer the following questions a. What are the values you read after it completes its rotation Ladybug:  = _ 721.25 degree,  = _ 100 degrees/s, v = _ 3.491 m/s Beetle:  = __ 720.89 degree,  = __ 100 degrees/s, v = _ 5.344 m/s b. Click on “radians” and write the values you read Ladybug:  = _ 12.59 rad,  = _ 1.745 rad/s, v = _ 3.491 m/s Beetle:  = __ 12.58 rad,  = _ 1.745 rad/s, v = _ 5.344 m/s c. What are the angular and centripetal accelerations Ladybug: a R = _ 4.062 m/s 2 ,  = _ 0.1209 rad/s 2 Beetle: a R = _ 9.519 m/s 2 ,  = _ 0.1210 rad/s 2 3. Set the ladybug default position by clicking “Reset All” and enter an angular velocity of 50 degrees/second. Running the simulation, you will be able to find the following position versus time graph. What are the positions of the ladybug at the following scenario  = _ 179.6 degree ,  = _ 3.135 rad  = _ 259.793 degree ,  = _ 4.534 rad 4. What are the speed, velocity and accelerations of the ladybug in question 3? a. V ladybug = -1.396x10^-2 m/s, v xladybug = 1.395x10^-2 m/s, v yladybug = -1.95x10^-4 m/s, a ladybug = -2 m/s 2 b. V ladybug = 1.968 m/s, v xladybug = 0.89 m/s, v yladybug = _ 1.753 m/s, a ladybug = 0.35 m/s 2 5. If the beetle located at 3 m from the center of the turntable when it starts its motion at 0 0 , what are the position, speed, velocity and accelerations of the beetle at the following scenario? a.  = _ 262.6 degrees,  = _ 4.58 radians b. V beetle = 2.675 m/s, v xbeetle = 0.333 m/s, v ybeetle = -3.052 m/s, a beetle = 2.338 m/s 2 b) c) d) a)

P hy s i c s L a b ( O n l i n e S i m u l a t i o n ) Procedure II: Angular Kinematics: 1. Click “Reset All” and check the position of the ladybug on the turntable. Under the “Show graphs” select  ,  ,  graph and set the angular acceleration in such a way that the turntable moves counterclockwise. What are the directions of velocity and accelerations after the turntable rotates 180 0 2. Click “Reset All” again and this time drag the Beetle on the turntable and put it at (3,0). Set the angular velocity to 0 rad/s and angular acceleration to 2 rad/s 2 . Now click “Go” and stop it after the turntable rotates for 10 seconds. Make sure you use different options of the graphs under the “Show graphs” options to answer your question below a. What are the values you read at the 5th second? Ladybug:  = 24.879 rad, v = _ 10.05 m/s, a = _ 2 m/s 2 Beetle:  = _ 25.126 rad, v = _ 10.05 m/s, a = __ 2 m/s 2 b. Calculate the following velocity and accelerations at the 5 th second Ladybug: v tan = _ 270.504 m/s, a tan = _ 54.10 m/s 2 Beetle: v tan = _ 273.105 m/s, a tan = _ 54.621 m/s 2 c. Calculate the total acceleration and compare it with the values you found in a Ladybug: a = _ 54.136 m/s 2 Beetle: a = _ 54.65 m/s 2 __________________________________________________________________ __________________________________________________________________ 3. Answer the following questions based on the graphical information below. You can try to check it with running a simulation b) c) d) a) a. What is the angular acceleration? 1.4deg/sec^2 b. What is the angular velocity at t=0? 10 c. What is the angular displacement of of the platform at 5 seconds? 75 d. Where was the initial location of the ladybug? (as measured from the center of axis of rotation) 0 e. What is the tangential velocity at t = 5 s? 0.698 f. What is the tangential acceleration at t = 5 s 0.0608 g. What is the total acceleration at t = 5 s 0.70

P hy s i c s L a b ( O n l i n e S i m u l a t i o n ) c. A ladybug is clinging to the rim of a wheel, which is spinning counterclockwise and is speeding up Since it is speeding up so magnitude of velocity increases and magnitude of acceleration increases, but direction remains same. 2. Set the angle and the angular acceleration to zero. Set the angular velocity to 2.0 rad/s. Predict how far the ladybug will rotate in radians after 5.0 s. Check your prediction with the simulation. Was it correct? The ladybug will rotate for 10.0 rad in 5.0s for the initial angle and angular acceleration zero and change the angular velocity for 2.9 rad/s 3. Set the angle to 5.0 rad and the angular acceleration to zero. Set the angular velocity to 3.5 rad/s. Predict the angle at which the ladybug will be at after 4.5 s. Check your prediction with the simulation. Was it correct? The ladybug will rotate for 20.75 rad in 4.5 s for an initial angle of 5.0 rad, an angular acceleration of zero and an angular velocity of 2.0 rad/s. 4. Set the angle to zero, the angular velocity to 2.0 rad/s, and the angular acceleration to be 0.30 rad/s 2 . Predict how fast the ladybug will rotate after 5.0 s. Check your prediction with the simulation. Was it correct? The ladybug will rotate for 3.5 rad in 5.0s for an initial angle and angular acceleration of 0.3 rad/s^2

P hy s i c s L a b ( O n l i n e S i m u l a t i o n )