phy 133 lab 4

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Jan 9, 2024

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Anubrota Majumdar 4/30/2023 PHY 133 Circular Motion Lab Report
INTRODUCTION: - The objective of the "Circular Motion" lab is to analyze the iolab cart's circular motion using its location, speed, and acceleration. The angle of rotation, measured in radians or rotations, is the most appropriate way to describe the distance covered by the rotating motion. We will measure the device's angular velocity as it spins and also determine the tangential acceleration at point A on the iOlab gadget. The angular velocity will be expressed in radians per second, while the acceleration will be expressed as radians per second squared. To ensure consistency, we aim to spin the iOlab cart at the same speed throughout the experiment. The tangential velocity of the circular motion depends on the distance between the point of interest and the rotational center and is calculated using the equation v = r ? . Additionally, we will examine the magnitude of the centripetal acceleration, which is expressed using the formula a ? = v²/r, where r is the circular motion's radius and v is its tangential velocity. We will use the iOlab's gyroscope and accelerometer sensors to measure the linear acceleration and angular velocity at point A. The motion being analyzed in this lab is expected to have a constant angular velocity, allowing us to determine the distance between point A and the device's center for comparison with the measured value. We predict that the values obtained from the graph will be lower than the lab-measured distance.
FORMULAS USED: - Distance covered by the rotating motion: The angle, expressed in rotations or radians Tangential speed: v = r ? , where v is the tangential velocity, r is the distance between the point of interest and the rotational center, and ? is the angle of rotation Centripetal acceleration: 𝑎? = ? ²/ ? , where a is the magnitude of the centripetal acceleration, v is the tangential velocity, and r is the radius of the circular motion Angular velocity: expressed in radians per second. Linear acceleration: measured using the iOlab's gyroscope and accelerometer sensors at point A. APPARATUS USED: - Required Apparatus: iOlab device Screw Scotch tape Masses of varying weights Flat surface to place the iOlab device. Computer to connect and record data from the iOlab device.
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PROCEDURE:- Use a measuring tape to determine the distance between the center of mass (point G) and the accelerometer (point A) on the iOlab device. Make the iOlab gadget spin around its z-axis by gently tossing it in the air and gradually increasing the force used to toss it. Calculate the centripetal acceleration by finding the square root of the x compound squared plus the y compound squared, then use vector addition to obtain the total centripetal acceleration. Analyze the data collected for each speed of tossing the object to determine the angular speed of the iOlab device while it was in the air. Plot the relationship between centripetal acceleration and angular velocity (ac vs. ω) as well as the relationship between centripetal acceleration and angular velocity squared (ac vs. ω^2) after collecting and analyzing all data. Calculate the radius of rotation and compare it to the distance measured between point G and point A. OBSERVATIONS: - Angular Velocity of the iolab after spinning it once (angular speed 1)
Angular Velocity of the iolab after spinning it once (angular speed 2) Angular Velocity of the iolab after spinning it once (angular speed 3)
GRAPHS: - 15 20 25 30 35 0 5 10 15 20 25 30 35 40 45 ac vs ω This is a graph representing the data for the relationship between ac vs. ω X Y ω(rad/s) ac(m/s^2) -16.18 10.5 -30.5 36.8 -33.9 41.9
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200 300 400 500 600 700 800 900 1000 1100 1200 0 5 10 15 20 25 30 35 40 45 f(x) = 0.04 x + 1.4 ac vs ω^2 This is a graph representing the data for the relationship between ac vs. ω^2 X Y ω^2(rad^2/s^2) ac(m/s^2) 261.7924 10.5 930.25 36.8 1149.21 41.9
Calculations: Ac of angular speed 1: Ac of angular speed 1: = √ (3.982) ² + (-10.297) ² = 11.029 Ac of angular speed 2: = √ (13.347) ² + (-34.727) ² = 37.141 Ac of angular speed 3: = √ (15.474) ² + (-39.298) ² = 42.295 The radius = 4cm or 0.04m Now, finding the error: - % error =| (0.0353-0.04)/ (0.04) x 100 |= 11.75% for the first graph % error =| (0.0363-0.04)/ (0.04) x 100 |= 9.25% for the second graph DISCUSSION: - In this lab, we investigated the relationship between ac = v^2/r and v = r, which are essential in understanding circular motion. We collected data using the iOlab device and analyzed it to draw conclusions about the relationship between these variables.
We plotted the data and generated trendlines to visualize the correlations. The first graph shows the graph of ac versus ω, where ω is the angular speed of the iOlab device. We estimated the distance between points A and G to be 0.0353 m, and the graph showed a power series trendline. On the other hand, the second graph shows the graph of ac versus ω^2, where we estimated the distance between points A and G to be 0.0363 m. This graph displayed a linear trendline. We also noted that the x and y compounds of acceleration are typically positive and negative, respectively. This observation is consistent with the way the iOlab gadget was held during the rotation. We found the radius of rotation to be 0.04 meters. Finally, we calculated the percent error for ac versus ω and ac versus ω^2 to be 11.75% and 9.25%, respectively. These values fall within the acceptable range, indicating that the data we collected is reliable.
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