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Ladybug Circular Motion Formal Lab Write UpJustin Carbary 6th HourINTRODUCTION:The ladybug circular motion lab presented by Phet is designed to allow the user to understand mathematically and physically the representation, or relationship, that correlate angular velocity, radius, velocity, and acceleration all together in one with some background knowledge that was taken in classes prior to the lab.EXPERIMENTAL PROCEDURE:Search online and open the Phet simulation titled “Ladybug Revolution”Draw your prediction on the turntable of the velocity and acceleration vectors of the ladybug on the turntable at any point. ?(Notice: The view online is an overhead view)Once down making your prediction, click the intro tab up top and make sure that both the “show velocity vector” and “show acceleration vector” are checked in the boxThe ladybug can be moved around the turntable by clicking and dragging the clip art ladybugSet the ladybug in a similar position as the first image on your lab image. ?Then enter in a velocity of 150 degrees/second. ?Illustrate your results below on the second turn table below of the velocity and acceleration vectors.Now click on the rotation tabBring up the ruler and move the bug so that it is at 2mm from the center and then remove the ruler. ?(Notice: The ruler is labeled in mm but for the sake of the lab it will represented in meters)Running multiple tests with different ranging angular velocities, record your data in the table given in your lab packetTo get acceleration, under “Show graphs”, click theta, omega, accelerationTo get velocity, under “Show graphs”, click theta, omega, velocityRepeat step 8 using a radius of 3 and fill out the second table given on the lab packetEXPERIMENTAL DATA:First Recorded Table with Radius of 2 metersAngular VelocityRadiusVelocityVelocity ^ 2Acceleration1 rad/sec2m2.315 m/s5.36 m/s2.315 m/s^22 rad/sec2m4.629 m/s21.428 m/s9.259 m/s^23 rad/sec2m6.944 m/s48.219 m/s20.832 m/s^24 rad/sec2m9.259 m/s85.729 m/s37.035 m/s^2Second Recorded Table with Radius of 3 metersAngular VelocityRadiusVelocityVelocity ^ 2Acceleration1 rad/sec3m2.944 m/s8.667 m/s2.944 m/s^22 rad/sec3m5.888 m/s34.668 m/s11.776 m/s^23 rad/sec3m8.832 m/s78.004 m/s26.497 m/s^24 rad/sec3m11.776 m/s138.674 m/s47.105 m/s^2Analysis:Table One CalculationsVelocity GivenCalculation to Find Velocity^22.315 m/s2.315^2 = 5.36 m/s4.629 m/s4.629^2 = 21.428 m/s6.944 m/s6.944^2 = 48.219 m/s9.259 m/s9.259^2 = 85.729 m/sTable Two CalculationsVelocity GivenCalculation to Find Velocity^22.944 m/s2.944^2 = 8.667 m/s5.888 m/s5.888^2 = 34.668 m/s8.832 m/s8.832^2 = 78.004 m/s11.776 m/s11.776^2 = 138.674 m/sDo you notice any relation between the velocity^2, radius, and acceleration?There exists a relationship between the three variables mentioned above. ?That relationship can be written in an equation that goes:Acceleration = Velocity^2????????????????????????RadiusExample: ??The last data set in table two. ?Acceleration in the table = 47.105 m/s^2. ?Radius =3m. ?Velocity^2 (calculated) = 138.674 m/s47.105 m/s^2 = 138.674 m/s???????3m47.105 m/s^2 = 46.2247 m/s^21.86% Error*Error may be due to rounding values altering results slightly or rounding did not go far enough out to get nearer exact answers equaling the same. ?Errors may occur in all values as of rounding and human misread of certain steps may result in slightly ascue data*From the graphs do you notice the magnitude of the velocity or the magnitude of acceleration changing as angular velocity stays the same, if so how?Yes, the x and y component vectors for acceleration and velocity change but the total value stays the same for it always.In linear motion, when you have a constant acceleration, how does this affect the velocity? Is this different from circular motion? Explain.In linear motion, velocity increases. ?In circular motion, velocity does not change because it is a vector and is constantly changing direction whereas linear goes in a straight line and keeps the same direction. CONCLUSION:Results were obtained from the lab online. ?After setting the angle and angular velocity, hitting record and waiting for five seconds would record the acceleration and velocity. ?By switching between omega, theta, acceleration/ or velocity, you could visually see the value given and then you recorded that data in the table. ?The goal of the lab, was to determine a relationship between angular velocity, radius, velocity, velocity^2, and acceleration. ?The final result of the lab was just that. ?It was figured out that the equation that represents the relationship between the data values is, acceleration equals velocity squared divided by the radius of the object rotating. ?Through the animation and live recording graphs, the lab was also able to give insight on other aspects of angular motion, which is the current unit on, in preparation for the test of angular motion. ?In all, the lab did more than help form the equation mentioned above. ?It helped further understandable knowledge on things angular motion. ................
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