Kendall Widdel - Lab 6

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Dec 6, 2023

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Name: Kendall Widdel E-mail address: kwiddel@vols.utk.edu Laboratory 6 Report The purpose of this experiment is to understand rotational motion of extended objects and to experiment with angular acceleration. Experiment 1  time it takes to complete 5 rotations 10.32 seconds  distance from the shoulder to the elbow 11 inches  distance from the shoulder to the middle of the hand 24 inches  How far in degrees did the hand travel during the five rotations? 1800 degrees total  How far in radians did the hand travel during the five rotations? 31.42 radians  How far in meters did the hand travel during the five rotations? 0.486 m  What was the average angular speed (deg/s and rad/s) of the hand? 3.04 rad/s and 174.42 deg/s  What was the average linear speed (m/s) of the hand?

1.85 m/s  What was the average angular acceleration (deg/s 2 and rad/s 2 ) of the hand? How do you know? 3.04/10.32 = 0.29 rad/s^2 174.42/ 10.32 = 16.9 deg/s^2  What was the average centripetal acceleration (m/s 2 ) of the hand? 5.6 m/s^2 ELBOW  How far in degrees did the elbow travel during the five rotations? 1800 degrees total  How far in radians did the elbow travel during the five rotations? 31.42 radians  How far in meters did the elbow travel during the five rotations? 8.76m  What was the average angular speed (deg/s and rad/s) of the elbow? 3.04 rad/s 174.4 deg/s  What was the average linear speed (m/s) of the elbow? 0.8488 m/s

 What was the average angular acceleration (deg/s 2 and rad/s 2 ) of the elbow? How do you know? 3.04/10.32 = 0.295 rad/s^2 174.4/10.32 = 16.899 deg/s^2  What was the average centripetal acceleration (m/s 2 ) of the elbow? 2.58 m/s^2  Which quantities are different and which quantities are the same for the hand and the elbow? The quantities that are the same are the degrees traveled and the radians traveled, and the average angular speed and average angular acceleration. The distances, the average linear speed and the average centripetal acceleration were all different.  Describe the direction of those arrows, while the angular speed of the wheel is increasing, constant, or decreasing. The directions of the arrows when increasing cause them to go perpendicular, when constant the arrows stay the same, and when they are decreasing, the arrows become smaller and move further away from the center of the circle. o Click Go let the simulation run for approximately 10 seconds. o What is the magnitude and direction of the torque on the wheel?  Magnitude is 6 Newtons meters in a direction tangential to the circle while the direction of torque is perpendicular to the center of the circle o What happens to the lady bug?  The lady bug flies off the wheel o What provides the centripetal force to keep the bug moving in a circle?  The centripetal force is provided by the frictional forces

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o Why does this eventually fail?  This eventually fails because there are limits when it comes to frictional forces and will eventually end causing it to fail. o Observe the acceleration vector after you click Go. How does it change?  The acceleration vector starts small and does not point at the center but after it rotates two times it eventually points at the center and increases the magnitude o Will the acceleration vector ever point directly to the center? Why or why not?  Yes because it starts pointing away but eventually will point directly to the center and stays there  What happens to the acceleration vector? The acceleration vector decreases in magnitude once a break force is applied and moves away from the center of the circle  Use the ruler to measure the radius r of the boundary between the green and pink circles. Record r in your log. R=2.9m  Calculate what the tangential component of the applied force must have been. Record F tang in your log. 2.8 Newtons  Compare the torque τ and the angular acceleration α and calculate the moment of inertia I of the disk from τ = Iα. Record I in your log. I= 1kg*m/s^2

 Compare with the moment of inertia displayed in the graph. Record the comparison in your log. 1kg*m/s^2  Set the inner radius equal to 2. Find the moment of inertia for this shape. Record it. 1.25 kg*m/s^2  Even when the force on the platform changes, the moment of inertia graph remains constant. Why? The moment of inertia graph remains constant because the torque and the angular acceleration are positively related. Because one does not change, means the other does not either, meaning the inertia stays constant  While the disk is moving, change the inner radius to 2 m. What happens to the moment of inertia and the angular velocity? The moment of inertia increases by .25kg*m/s^2 and the angular velocity decreases buy 0.2 radians/s  Make some more changes to the inner radius, outer radius and mass of the disk. Describe what happens. The mass of the disk increases, the moment of inertia increases, the outer radius decreases, the angular velocity decreases, and the inner radius increases. Experiment 2 weight of meter stick and clips -2.5 force sensor reading when stick is again horizontal -1.5 weight suspended from left clip distance from left clip to CM of the meter stick 0.47m

distance from force sensor hook to CM of meter stick 0.27 m distance d from force sensor hook tothe left clip 0.8 Modeling the meter stick as a forearm and the force sensor as the biceps, compare the force that the biceps has to exert to keep the forearm horizontal to the force it has to exert to just support the weight of the forearm. Comment on the relative magnitude of these forces. The relative magnitude of these forces add about 1.5 amount of weight of the meterstick List all the forces (magnitude and direction) acting on the forearm (meter stick) and calculate all the torques (magnitude and direction) exerted by those forces about the pivot point, when the stick is horizontal and in equilibrium. Do all the torques cancel out? The forces acting on the forearm would be the force of 1.5 in the downward direction, the center of gravity of a force of 1 in the downward direction. The torque of -.27 m to the left and the center of gravity being -.27m to the left. Therefore yes these torques cancel out. Reflection This experiment was hard to follow doing it by myself, and would have been better demonstrated in videos as I believe I did some parts of it wrong. The calculations were hard to figure out and took some research to complete them.

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