4 Circular-Motion Online

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Jan 9, 2024

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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 ) Introduction: We have seen the kinematics equations for translational motion in “Kinematics in one dimension” simulation. In this simulation we are dealing with rotational kinematics. If the motion is pure rotation, the equations can easily be rewritten by changing the translational symbols to rotational. The symbols and the rotational kinematics equations are given below. Angular displacement: units used for angle are degrees and radians. Linear quantities can be related to angular quantities as shown in the table to the left. Procedure I - Uniform Circular Motion: Open Ladybug Revolution http://phet.colorado.edu/simulations/sims.php?sim=Ladybug_Revolution 1. Click “Reset All” and check the position of the ladybug on the turntable. Set the angular velocity in such a way that the turntable moves clockwise. What are the directions of velocity and accelerations after the turntable rotates 180 0 ? R aR at ¿ d / dt ¿ d / dt ´ ❑ = ¿ t ´ ❑ = ¿ t ¿ ❑ 0 + ´ ❑ ( t − t 0 ) ¿ ❑ 0 + ´ ❑ ( t − t 0 ) ❑ 2 = ❑ 0 2 + 2 ´ ❑ ( x − x 0 ) ¿ ❑ 0 + ❑ 0 ( t − t 0 ) + 1 2 ´ ❑ ( t − t 0 ) 2 As you see the figure on the left, the ladybug is located R from the center of axis of rotation. Its tangential velocity (v t ), tangential acceleration (a t ), centripetal acceleration (a R ), and combined (resultant) acceleration (a) are specified. The equation for centripetal and combined accelerations are given by a R = v 2 R a = √ a R 2 + a t 2 Translational Angular Displacement x  x =  R Velocity v  v t =  R Acceleration a  a t =  R

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