Lab 7 Rotation PDF

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Physics 110 Online Lab 7 Rotation...

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Introductory Physics Rotation Abstract:

Hunter College

Rotational motion describes motion of an object around a circular path. As always with motion, rotational motion has similar resemblances with linear motion with vector quantities like velocity, displacement, acceleration. In rotational motion these vector quantities are referred to as angular velocity, angular displacement, and angular acceleration. Their units are different as well replacing meters from linear motion with radians for rotational motion. Rotational motion also has a moment of inertia which resembles mass in linear motion. Moment of inertia is a quantity represented by an objects tendency to resist angular acceleration and is dependent on mass and related to how mass is distributed. Moment of inertia is also dependent on the distance from the axis of rotation. Torque is the rotational motion equivalent of linear motion’s force. Torque is dependent on moment of inertia and angular acceleration, Torque =I x alpha. Rotational motion also includes angular momentum (L) which is also dependent on moment of inertia and angular velovity (L=Iw). Through simulations and calculations, we are able to test the relationships between linear and rotational motion and prove the dependency of moment of inertia on torque and angular momentum Part I: Rotation Procedure https://phet.colorado.edu/sims/cheerpj/rotation/latest/rotation.html? simulation=rotation 1, Open the simulation and click on ‘Rotation’ tab.

1. Setup Angle Units: degrees Set Angular Velocity: 10 Show graphs: θ, ω, x, y Adjust the scaling settings on the right side to make sure the data will be displayed properly on your screen.

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2.At time 0



Record θ, ω, x, y in the data table. Switching the graph to get the values for angular acceleration α, velocity v, and linear acceleration a. Calculate the radius r from x and y. X= 2, y=0 r2 =x2+y2 r 2= 4 + 0 r= rad (4) r=2m



Calculate the v2/r

 

V= 0 02 / 2 = 0 m/s2 3. Reset the graph to θ, ω, x, y and click on the Go! 4. Click on the Stop after 5 s, take screenshot of your screen and complete the data table below.

5. Click on the clear button. Drag the ladybug to the position x=4 m and y=0 m. Repeat step 1 to 4. 2. X= 4, y=0 r2 =x2+y2 r2= 16 + 0

r= rad (16)

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at t=0 V= 0 02 / 4 = 0m/s2

Data Table 1 Make sure to put units into the table. Y X Time Θ Ω m degre degree m s/s es 0s 0 10 2 0

0

5s

49.46

10

1.3

1.52

0

0s

0

10

4

0

0

5s

49.62

10

2.57 4

3.02 8

0

α rad/s

v m/s

a m/s2

r m

v2/r

0.34 9 0.34 9 0.69 4 0.69 4

0.06 1 0.06 1 0.12 1 0.12 1

2

0.06 1 0.06 1 0.12 1 0.12 1

2

2 4 3.97

Analysis 1. From the screenshot, explain the x and y positions. What are mathematic functions can be used to describe those?

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X and y positions allow for the radium to be found. Through using the equation of a circle at the origin, r2 =x2+y2 can be used to determine radius which is integral for further calculations. 2. Why is angular acceleration zero? Why the linear acceleration is not zero? Angular accelerations is zero because angular velocity is a constant number of 10. Since there is no change in angular velocity over time there is no acceleration. Linear acceleration however occurs because there is a change in linear velocity. 3. When you change the position of ladybug, which variable are changed and why? The radius is changed because the ladybug is moving in a circular motion, and when the position is changed, only its horizontal position changes to x=4, so its horizontal displacement from the origin is representative of the radius. Since radius changes this impacts linear velocity which later impacts linear acceleration. 4. What are the directions of linear acceleration and the linear velocity? Linear acceleration and linear velocity are tangent to the rotational motion. 5. What are the angular velocities in radians? Calculate the angles in radians (at 5 seconds) from the angular velocities. For first simulation at 5s  49.46 (pi/180) = 0.863 For first simulation at 5s 49.62 (pi/180) = 0.866 6. 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 5 s. Check your prediction with the simulation. Was it correct? Initial theta is 5, change in time = 5 seconds 3.5 = (x-5)/5 17.5 = x-5 X = 22.5 radians (calculated value) Simulation yielded: 22.36 rad (Close enough) prediction was somewhat correct. 7. If the ladybug is on the 4m rim, use the simulation to find the minimum angular velocity that the ladybug will fly off the wheel? Calculate the maximum static friction coefficient between the bug and wheel?

Minimum angular velocity = 3.5 rad Ff = u(Fn) = (u)g F= m(v^2/r) (u)g = mv^2/r) (u) = 0.121/ 9.8 = 0.0123

Part II: Moment of Inertia Procedure https://phet.colorado.edu/sims/cheerpj/rotation/latest/rotation.html? simulation=torque 1. Open the simulation and click on ‘Moment of Inertia’ tab.

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2. Set the torque to 1 N. Change only one variable each time from the Base trial. 3. Adjust the scaling settings on the right side to make sure the data will be displayed properly on your screen. 4. Click on Go and run for 2.5 seconds and stop the simulation. 5. Generate screenshots and record the data for the table below.

1

Data Table 2 Make sure to put units into the table. Change of I from Base Trial

Change of α from Base Trial

1

0

0

35.305

1.578

0.578

26.58

4

53.823

1.065

0.065

3.477

0

2

229.183

0.25

0.75

171.883

0

4

114.592

1

0

57.292

Trial

Torque

Mass

Radius (inner)

Radius (outer)

Base trial Increase Mass Increase Inner Radius Decreas e Outer Radius Increase Torque

1N

0.12 kg

0m

4m

rad/s2 57.30

1N

0.20 kg

0

4

1N

0.12

1.02

0.5N

0.12

2N

0.12

Angular accelerati on (α)

Moment Inertia (I) Kgm^2

of

Change mass:

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Change inner radius

Change

outer

radius:

Increase Torque:

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Analysis From the screenshots and table above, explain the following: 1. How does mass affect moment of inertia? and why? Moment of inertia is dependent on mass. How the mass is distributed relative to the axis of ration is also very important. Increasing the mass will have increase moment of inertia because as seen above when mass was increased to 0.20 grams, moment of inertia increased from 1 to 1.578. 2. How does mass distribution affect moment of inertia? and why? Moment of inertia is dependent on mass distribution. If the mass is further away from axis of rotation, then mass will carry more momentum with it increasing moment of inertia. If mass is closer to outer radius, then moment of inertia decreases. 3. When you increase the Torque, what kinds of effects do you observe? Explain why? Torque is necessary to give a rotating object a certain a certain angular acceleration which is also dependent on moment of inertia. If torque is increased angular acceleration should increase as well. As seen above when torque was increased by 1N, acceleration nearly double.

Part III: Angular Momentum Procedure 1. Open the simulation and click on ‘Angular Momentum’ tab. 2. Set the Angular velocity to 20 degrees/s.

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3. Drag the Inner Radius from 0 to 4 m and take screenshot at the end.

4. You should see some changes in angular velocity and Moment of Inertia. If it is not, adjust the scaling on the right to show the data on the screen.

Analysis 1. What is the SI unit for angular momentum? kgm2/s 2. Calculate the angular momentum in SI units? L=IW 10 degrees (pi/180) = 0/1745rad L=2x0.174 L=0.349 kgm2/s 3. Explain why the Angular Velocity changes. Angular velocity changes due to object changing its shape, the inner radius increasing allowing moment of inertia to change. Does Angular Momentum change? Why? No angular momentum does not change, it can only change if acted upon by an external applied torque.

Post-Lab Page 10 of 11

1.The diagram shows a top view of a child of mass M on a circular platform of mass 5M that is rotating counterclockwise. Assume the platform rotates without friction. Which of the following describes an action by the child that will result in an increase in the total angular momentum of the child-platform system?

(A) The child moves toward the center of the platform. (B) The child moves away from the center of the platform. (C) The child moves along a circle concentric with the platform (thin line shown) opposite the direction of the platform's rotation. (D) None of the actions described will change the total angular momentum of the child-platform system. 2. A solid disk with a mass of 1.0 kg and a radius of 0.25 spins at an angular velocity of 10 rad/s. A string that wraps around the edge of the disk applies a 2.0 N force tangent to the disk, for 0.5 seconds. What is the new angular velocity? r=0.25 wo = 10 rad/s m=1kg t= 0.5s wf=wo+ alpha(t) ½ (1)(0.252) = 0.03125 Alpha = (2)(0.25) / 0.03125 = 16rad/s2 wf = 10 + 16(0.5)

wf= 18 rad/s

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