first name (print) last name (print) brock id (ab17cd) (lab date) A friendly reminder: Is this your scheduled experiment? See the previous page.

Size: px
Start display at page:

Download "first name (print) last name (print) brock id (ab17cd) (lab date) A friendly reminder: Is this your scheduled experiment? See the previous page."

Transcription

1 (ta initials) first name (print) last name (print) brock id (ab17cd) (lab date) Experiment 2 Angular Motion A friendly reminder: Is this your scheduled experiment? See the previous page. In this Experiment you will learn some basic principles of rotational motion around a central pivot point to measure the specific rotational inertia I d of a solid disc by a multistep method to manipulate equations and have them disclose information of interest to you to use a computer-based fitting program to enhance the analysis of your data to apply error analysis to experimental results and thus make your results relevant. Prelab preparation Print a copy of this Experiment to bring to your scheduled lab session. The data, observations and notes entered on these pages will be needed when you write your lab report and as reference material during your final exam. Compile these printouts to create a lab book for the course. To perform this Experiment and the Webwork Prelab Test successfully you need to be familiar with the content of this document and that of the following FLAP modules ( Begin by trying the fast-track quiz to gauge your understanding of the topic and if necessary review the module in depth, then try the exit test. Check off the box when a module is completed. FLAP PHYS 1-1: Introducing measurement FLAP PHYS 1-2: Errors and uncertainty FLAP MATH 1-4: Solving equations FLAP MATH 1-6: Trigonometric functions Webwork: the Prelab Angular Motion Test must be completed before the lab session! Important! Bring a printout of your Webwork test results and your lab schedule for review by the TAs before the lab session begins. You will not be allowed to perform this Experiment unless the required Webwork module has been completed and you are scheduled to perform the lab on that day.! Important! Be sure to have every page of this printout signed by a TA before you leave at the end of the lab session. All your work needs to be kept for review by the instructor, if so requested. CONGRATULATIONS! YOU ARE NOW READY TO PROCEED WITH THE EXPERIMENT! 10

2 11 Torque acting on a rotating body To understand what torque is, let us consider a rigid body with its centre of mass at a point r = 0, constrained to rotate about that point. The radius vector r of a point on the body has the origin at r = 0 and ends at the point, a distance r from the origin, as shown in Figure 2.1. If a force F is applied at that point, in the plane of rotation of the disc, at a distance r from the centre, and at an angle φ to the radius vector r, the magnitude of the turning torque τ produced by this force is: τ = rf sinφ (2.1) The torque τ depends both on the distance from the centre of rotation and on the direction of the applied force F. Decomposing F into a radial component F r and a tangential component F t so that F = F r + F t, it can be seen that only the tangential component of F causes torque and affects the magnitude of τ. A force applied through the centre of rotation has a zero tangential component (φ = 0,F t = 0) and the radial component alone produces no torque and will not cause angular acceleration. As the angle of the force changes, so Figure 2.1: Rotational coordinates does the torque experienced by the body; for a given magnitude of the force, F, the maximum torque is produced when F = F t is perpendicular to r and τ = rf t = rf. Resisting the force F is the total mass M of the rotating body. Suppose that this mass consists of many particles of mass m i so that M = i m i. In a translational motion, the force acts equally on all the component particles of the body at once, according to Newton s second Law F = i (m i a) = M a. In a rotation, the rotational effect of F on a particle is proportional to the distance r from the centre of rotation. While the entire rigid body experiences a single angular accelaration α, common to all its particles, each of them will experience a tangential acceleration a i that is proportional to the distance r i from the centre of rotation. The rotational moment of inertia I of a rigid body composed of many particles is simply the sum of the individual rotational moments of inertia of all particles: I = i m i r 2 i (2.2) For a thin hoop, where all the particles are located at the same common radius away from the centre, r i = R, Eq. 2.2 reduces to I = MR 2 ; for other shapes, the calculation may not be so simple. The rotational form of the Newton s Second Law is τ = Iα: F = i (m i a) = Ma τ = i (m i ri 2 α) = Iα. The torque τ plays the same role for rotational motion that the force F plays for translational motion. Determining the rotational inertia of a disc Consider a homogeneous disc of radius R and mass M constrained to rotate without friction around the centre of mass. A massless string is wrapped around the outer edge of the disc and connected to a mass m that is subjected to the force of gravity F g, as shown in Figure 2.2. The string experiences a tension T

3 12 EXPERIMENT 2. ANGULAR MOTION due to the weight of m; at the other end of the string the same tension T acts on the edge of the disc at a distance r from the centre of rotation. The displacement of the falling mass is given by Equation 2.3: y = y 0 +v 0 t+at 2 /2 (2.3) When a force is applied, the disc, initially at rest, begins to spin as m falls with linear acceleration a = g T m. (2.4) The rotational acceleration of the disk is α = a r = τ I = Tr I. (2.5) By combining Eqs. 2.4 and 2.5, the rotational inertia I of the disc can be expressed in terms of a as follows: I = mr 2( g ) a 1. (2.6) Measuring the acceleration of the falling mass, and comparing it to the acceleration of the free fall, yields an operational measurement of the moment of inertia of the disk. Figure 2.2: A falling block causes the disc to rotate Procedure The rotational inertia I d of a steel disc will be determined indirectly in three steps: 1. measure the rotational inertia I c of a spinning cradle that will accept the disc; 2. measure the rotational inertia I t = I c +I d of the cradle and disc combination; 3. calculate I d from the difference of these two results. The cradle consists of a plastic disc bolted to a metal drum of four stacked pulleys of varying diameters. The cradle is centered on a ball-bearing post and can rotate nearly friction-free around this vertical axis as long as it is not rubbing against the side of the post. A string, wrapped around one of the drum pulleys and attached at the other end to a suspended mass m, allows a torque τ to be applied to the cradle at radius r of the pulley. The string leaving the drum must be perpendicular to the axis of rotation and to the radius vector, as shown in Figure 2.3. Figure 2.3: Experimental setup? Suppose that the string was not perpendicular. What adjustments, if any, would you need to make to your torque calculations?

4 13 The pulley A in Figure 2.3 is part of a photogate system. The C-shaped photogate has an infrared transmitter at one end and an infrared detector at the other end. As the pulley rotates, the spokes interrupt the beam, turning on and off the red light-emitting diode (LED). The LabPro device detects and counts these changes and Physicalab calculates the distance that the string has moved. The pulley has ten spokes and a circumference of 155 mm, so there are twenty pulses transmitted every rotation of the pulley. Each pulse represents a radial distance of 7.75 mm travelled by the string and hence the same distance y moved by the mass m. After the data acquisition is initiated, LabPro waits for the first transition and marks this event with the elapsed time and assigns it an initial distance y = 0. After all subsequent transitions, the new time and total distance travelled are sent. Note that the time t = 0 set by LabPro will not likely coincide with the start of the motion. Data gathering and analysis using Physicalab 1. Wrap the string, trying not to overlap the strands, around the second smallest pulley (r = m) on the cradle and arrange the string path as shown in Figure Place a weight m w on the mass holder and rotate the cradle to raise these to the top of the assembly. Hold the cradle in place by putting a weight on the edge of the platform.? Consider the geometry of the system, is the cradle likely to rub against the post? 3. Shift focus to the Physicalab software. Select Dig2, the channel that the photogate should be connected to, then choose to collect a nominal 20 points with 0.5 seconds between points. 4. Remove the weight from the platform. The cradle will begin to rotate. Press Get data to start gathering the photogate data. Note that the platform will not likely have a zero velocity v 0 = 0, at time t = 0 when the data acquisition begins.? Will this arbitrary starting point in your data collection have any effect on the quantity that you want to determine from the fit? 5. Stop the data acquisition and the platform rotation before the mass holder reaches the end of it s trajectory; it will save you the trouble of having to re-spool the string on the pulleys. 6. At the end of the run, review your graphed data; it should approximate a smooth curve that represents the falling of a mass m under constant acceleration a. If this is not the case, repeat the trial.? Could you delete a portion of your data set and still get the desired result from your fit? How might the result be affected by such a change? 7. Select fit to: y= and enter A+B*x+C*x**2/2 in the fitting equation box. Click Draw to perform a fit of your data. Click Send to: to yourself and your partner a copy of the graph for later inclusion in your lab reports.? How do you determine which of the fit parameters represents the acceleration a?

5 14 EXPERIMENT 2. ANGULAR MOTION m w (kg) a 1 (m/s 2 ) a 2 (m/s 2 ) a (m/s 2 ) Table 2.1: Acceleration data for unloaded cradle assembly Part 1: Determining the rotational inertia of the cradle Fill in Table 2.1, then calculate an average acceleration a for the various masses. You may now wish to evaluate the rotational inertia I c for the unloaded cradle, using Equation 2.6 and the value of a for a given m w in Table reftab:cradledata. This would not likely lead to the correct I c value because m in Equation 2.6 represents the total mass m = m w +m h m f that causes the tension T on the string. In your experiment, the effect of the applied mass m w and that of the mass holder m h is diminished by an unknown mass m f required to overcome the static and dynamic friction experienced by the platform and pulleys. You will have noted that the cradle sometimes begins to rotate with only the mass holder attached, when m w = 0. In this case, m h > m f and to prevent the system from rotating, m w would need to be negative (or the mass holder would need to be lighter). To get around the difficulty of not knowing m f, you could determine m h by weighing the mass holder, then use two sets of values from Table 2.1 and solve two simultaneous equations to eliminate the unknown variable m f. A better method makes use of the whole set of tabulated data values ( a,m w ) that are available while making unnecessary a knowledge of both m h and m f. Begin by rearranging Equation 2.6 so that m w is expressed as a function of a: I c = (m w +m h m f )r 2( g ) a 1 (m w +m h m f )r 2( g ) ( ) Ic m w = a gr 2 a+(m f m h ). (2.7) The simplification is valid only if a g so that (g/a 1) (g/a). Then the resulting equation is that of a straight line with slope I c /(gr 2 ) and y-intercept (m f m h ). Enter into an empty data window your set of ( a,m) coordinates. The scatter plot of your data should show a linear behaviour. Select fit to: y= and enter A+B*x in the fitting equation box. Click Draw and record below the fit parameters A and B along with their appropriate units. A =...±... B =...±... Calculate I c using Equation 2.7 and use the appropriate error propagation rules to evaluate the corresponding uncertainty I c : I c =... =... =...

6 15 I c =... =... =... I c =...±... Part 2: Determining the rotational inertia of cradle and disc Use the peg on the steel disc to center it on the cradle, then place a small piece of paper under the disc to prevent it from slipping. Repeat the previous steps to determine the rotational inertia I t of cradle-plus-disc. m w (kg) a 1 (m/s 2 ) a 2 (m/s 2 ) a (m/s 2 ) Table 2.2: Acceleration data for cradle assembly with disc A =...±... B =...±... I t =... =... =... I t =... =... =... I t =...±... Part 3: Determining the rotational inertia of the disc Subtract I c from I t to obtain I d, the rotational inertia of the disc alone. I d =... =... =... I d =... =... =... I d =...±... Measure the mass M and radius R of the steel disc. Also weigh the mass m h of the mass holder. M =...±... R =...±... m h =...±...

7 16 EXPERIMENT 2. ANGULAR MOTION Use the appropriate equation to calculate the theoretical rotational inertia for the disc that you used, as well an estimate of the error. I d(th) =... =... =... I d(th) =... =... =... I d(th) =...±... Perform a trial using the smallest pulley with pull mass m = 30 g on the unloaded cradle. Compare this a with the previous result for a obtained using the second smallest pulley and the same pull mass. The pulley radii from smallest to largest are: cm, cm, cm and cm. a(r = 1.539) =..., a(r = 2.282) =...? Do these two a values obtained by varying the pulley radius r agree with the results predicted by the theory? Lab report Go to your course homepage on Sakai (Resources, Lab templates) to access the online lab report worksheet for this experiment. The worksheet has to be completed as instructed and sent to Turnitin before the lab report submission deadline, at 11:00pm six days following your scheduled lab session. Turnitin will not accept submissions after the due date. Unsubmitted lab reports are assigned a grade of zero. Notes:...

8 17

first name (print) last name (print) brock id (ab17cd) (lab date)

first name (print) last name (print) brock id (ab17cd) (lab date) (ta initials) first name (print) last name (print) brock id (ab17cd) (lab date) Experiment 1 Capacitance In this Experiment you will learn the relationship between the voltage and charge stored on a capacitor;

More information

first name (print) last name (print) brock id (ab17cd) (lab date)

first name (print) last name (print) brock id (ab17cd) (lab date) (ta initials) first name (print) last name (print) brock id (ab17cd) (lab date) Experiment 5 Harmonic motion In this Experiment you will learn that Hooke s Law F = kx can be used to model the interaction

More information

Calorimetry and heat capacitance

Calorimetry and heat capacitance (ta initials) first name (print) last name (print) brock id (ab17cd) (lab date) Experiment 1 Calorimetry and heat capacitance In this Experiment you will learn some basic methods of heat exchange between

More information

first name (print) last name (print) brock id (ab17cd) (lab date)

first name (print) last name (print) brock id (ab17cd) (lab date) (ta initials) first name (print) last name (print) brock id (ab17cd) (lab date) Experiment 1 The pendulum In this Experiment you will learn the relationship between the period and length of an object swinging

More information

first name (print) last name (print) brock id (ab17cd) (lab date)

first name (print) last name (print) brock id (ab17cd) (lab date) (ta initials) first name (print) last name (print) brock id (ab17cd) (lab date) Experiment 5 Viscosity and drag In this Experiment you will learn that the motion of an object through a fluid is governed

More information

Angular Motion. Experiment 4

Angular Motion. Experiment 4 Experiment 4 Angular Motion Before starting the experiment, you need to be familiar with the concept of angular position θ, angular velocity ω, angular acceleration α, torque τ, moment of inertia I. See

More information

first name (print) last name (print) brock id (ab17cd) (lab date)

first name (print) last name (print) brock id (ab17cd) (lab date) (ta initials) first name (print) last name (print) brock id (ab17cd) (lab date) Experiment 2 Harmonic motion Prelab preparation Print a copy of this experiment to bring to your scheduled lab session. The

More information

Electron charge-to-mass ratio

Electron charge-to-mass ratio (ta initials) first name (print) last name (print) brock id (ab17cd) (lab date) Experiment 4 Electron charge-to-mass ratio In this Experiment you will learn the relationship between electric and magnetic

More information

Lab report 30 EXPERIMENT 4. REFRACTION OF LIGHT

Lab report 30 EXPERIMENT 4. REFRACTION OF LIGHT 30 EXPERIMENT 4. REFRACTION OF LIGHT Lab report Go to your course homepage on Sakai (Resources, Lab templates) to access the online lab report worksheet for this experiment. The worksheet has to be completed

More information

This is a reminder that Experiment 2 does not necessarily follow Experiment 1. My Lab dates: Exp.2:... Exp.3:... Exp.4:... Exp.5...

This is a reminder that Experiment 2 does not necessarily follow Experiment 1. My Lab dates: Exp.2:... Exp.3:... Exp.4:... Exp.5... Check your schedule! This is a reminder that Experiment 2 does not necessarily follow Experiment 1. You need to login to your course homepage on Sakai and check your lab schedule to determine the experiment

More information

Diffraction of light by a grating

Diffraction of light by a grating (ta initials) first name (print) last name (print) brock id (ab17cd) (lab date) Experiment 5 Diffraction of light by a grating In this Experiment you will learn the geometical analysis of a diffraction

More information

Rotational Dynamics. Goals and Introduction

Rotational Dynamics. Goals and Introduction Rotational Dynamics Goals and Introduction In translational dynamics, we use the quantities displacement, velocity, acceleration, mass and force to model the motion of objects. In that model, a net force

More information

first name (print) last name (print) brock id (ab17cd) (lab date)

first name (print) last name (print) brock id (ab17cd) (lab date) (ta initials) first name (print) last name (print) brock id (ab17cd) (lab date) Experiment 1 Archimedes principle Prelab preparation Print a copy of this experiment to bring to your scheduled lab session.

More information

τ = (Force)(lever arm) #

τ = (Force)(lever arm) # EXPERIMENT: MOMENT OF INERTIA OBJECTIVES : 1) To familiarize yourself with the concept of the moment of inertia, I, which plays the same role in the description of the rotation of the rigid body as the

More information

PHY 111L Activity 9 Moments of Inertia

PHY 111L Activity 9 Moments of Inertia PHY 111L Activity 9 Moments of Inertia Name: Section: ID #: Date: Lab Partners: TA initials: Objectives 1. Introduce moment of inertia for different objects 2. Understand the moment of inertia apparatus

More information

Physics 1050 Experiment 6. Moment of Inertia

Physics 1050 Experiment 6. Moment of Inertia Physics 1050 Moment of Inertia Prelab uestions These questions need to be completed before entering the lab. Please show all workings. Prelab 1 Sketch a graph of torque vs angular acceleration. Normal

More information

M61 1 M61.1 PC COMPUTER ASSISTED DETERMINATION OF ANGULAR ACCELERATION USING TORQUE AND MOMENT OF INERTIA

M61 1 M61.1 PC COMPUTER ASSISTED DETERMINATION OF ANGULAR ACCELERATION USING TORQUE AND MOMENT OF INERTIA M61 1 M61.1 PC COMPUTER ASSISTED DETERMINATION OF ANGULAR ACCELERATION USING TORQUE AND MOMENT OF INERTIA PRELAB: Before coming to the lab, you must write the Object and Theory sections of your lab report

More information

Rotational Dynamics Smart Pulley

Rotational Dynamics Smart Pulley Rotational Dynamics Smart Pulley The motion of the flywheel of a steam engine, an airplane propeller, and any rotating wheel are examples of a very important type of motion called rotational motion. If

More information

PHY 123 Lab 6 - Angular Momentum

PHY 123 Lab 6 - Angular Momentum 1 PHY 123 Lab 6 - Angular Momentum (updated 10/17/13) The purpose of this lab is to study torque, moment of inertia, angular acceleration and the conservation of angular momentum. If you need the.pdf version

More information

Rotational Motion. 1 Introduction. 2 Equipment. 3 Procedures. 3.1 Initializing the Software. 3.2 Single Platter Experiment

Rotational Motion. 1 Introduction. 2 Equipment. 3 Procedures. 3.1 Initializing the Software. 3.2 Single Platter Experiment Rotational Motion Introduction In this lab you will investigate different aspects of rotational motion, including moment of inertia and the conservation of energy using the smart pulley and the rotation

More information

Lab 9 - Rotational Dynamics

Lab 9 - Rotational Dynamics 145 Name Date Partners Lab 9 - Rotational Dynamics OBJECTIVES To study angular motion including angular velocity and angular acceleration. To relate rotational inertia to angular motion. To determine kinetic

More information

The purpose of this laboratory exercise is to verify Newton s second law.

The purpose of this laboratory exercise is to verify Newton s second law. Newton s Second Law 3-1 Newton s Second Law INTRODUCTION Sir Isaac Newton 1 put forth many important ideas in his famous book The Principia. His three laws of motion are the best known of these. The first

More information

Lab 11: Rotational Dynamics

Lab 11: Rotational Dynamics Lab 11: Rotational Dynamics Objectives: To understand the relationship between net torque and angular acceleration. To understand the concept of the moment of inertia. To understand the concept of angular

More information

Collisions and conservation laws

Collisions and conservation laws (ta initials) first name (print) last name (print) brock id (ab17cd) (lab date) Experiment 4 Collisions and conservation laws Prelab preparation Print a copy of this experiment to bring to your scheduled

More information

EXPERIMENT 7: ANGULAR KINEMATICS AND TORQUE (V_3)

EXPERIMENT 7: ANGULAR KINEMATICS AND TORQUE (V_3) TA name Lab section Date TA Initials (on completion) Name UW Student ID # Lab Partner(s) EXPERIMENT 7: ANGULAR KINEMATICS AND TORQUE (V_3) 121 Textbook Reference: Knight, Chapter 13.1-3, 6. SYNOPSIS In

More information

Activity P24: Conservation of Linear and Angular Momentum (Photogate/Pulley System)

Activity P24: Conservation of Linear and Angular Momentum (Photogate/Pulley System) Name Class Date Activity P24: Conservation of Linear and Angular Momentum (Photogate/Pulley System) Concept DataStudio ScienceWorkshop (Mac) ScienceWorkshop (Win) Momentum P24 Linear Angular.DS P28 Cons

More information

PHY 123 Lab 4 - Conservation of Energy

PHY 123 Lab 4 - Conservation of Energy 1 PHY 123 Lab 4 - Conservation of Energy The purpose of this lab is to verify the conservation of mechanical energy experimentally. Important! You need to print out the 1 page worksheet you find by clicking

More information

LAB 8: ROTATIONAL DYNAMICS

LAB 8: ROTATIONAL DYNAMICS Name Date Partners LAB 8: ROTATIONAL DYNAMICS 133 Examples of rotation abound throughout our surroundings OBJECTIVES To study angular motion including angular velocity and angular acceleration. To relate

More information

LAB 5: ROTATIONAL DYNAMICS

LAB 5: ROTATIONAL DYNAMICS 1 Name Date Day/Time of Lab Partner(s) Lab TA OBJECTIVES LAB 5: ROTATIONAL DYNAMICS To investigate and understand moment of inertia as it relates to rotational motion. To relate angular and linear position,

More information

Newton's 2 nd Law. . Your end results should only be interms of m

Newton's 2 nd Law. . Your end results should only be interms of m Newton's nd Law Introduction: In today's lab you will demonstrate the validity of Newton's Laws in predicting the motion of a simple mechanical system. The system that you will investigate consists of

More information

Experiment P28: Conservation of Linear and Angular Momentum (Smart Pulley)

Experiment P28: Conservation of Linear and Angular Momentum (Smart Pulley) PASCO scientific Physics Lab Manual: P28-1 Experiment P28: Conservation of Linear and Angular Momentum (Smart Pulley) Concept Time SW Interface Macintosh File Windows File rotational motion 45 m 500 or

More information

1. Write the symbolic representation and one possible unit for angular velocity, angular acceleration, torque and rotational inertia.

1. Write the symbolic representation and one possible unit for angular velocity, angular acceleration, torque and rotational inertia. ROTATIONAL DYNAMICS Pre-Lab Questions Page Name: Class: Roster Number: Instructor: 1. Write the symbolic representation and one possible unit for angular velocity, angular acceleration, torque and rotational

More information

6. Find the net torque on the wheel in Figure about the axle through O if a = 10.0 cm and b = 25.0 cm.

6. Find the net torque on the wheel in Figure about the axle through O if a = 10.0 cm and b = 25.0 cm. 1. During a certain period of time, the angular position of a swinging door is described by θ = 5.00 + 10.0t + 2.00t 2, where θ is in radians and t is in seconds. Determine the angular position, angular

More information

Lab Partner(s) TA Initials (on completion) EXPERIMENT 7: ANGULAR KINEMATICS AND TORQUE

Lab Partner(s) TA Initials (on completion) EXPERIMENT 7: ANGULAR KINEMATICS AND TORQUE TA name Lab section Date TA Initials (on completion) Name UW Student ID # Lab Partner(s) EXPERIMENT 7: ANGULAR KINEMATICS AND TORQUE 117 Textbook Reference: Walker, Chapter 10-1,2, Chapter 11-1,3 SYNOPSIS

More information

Rotation. PHYS 101 Previous Exam Problems CHAPTER

Rotation. PHYS 101 Previous Exam Problems CHAPTER PHYS 101 Previous Exam Problems CHAPTER 10 Rotation Rotational kinematics Rotational inertia (moment of inertia) Kinetic energy Torque Newton s 2 nd law Work, power & energy conservation 1. Assume that

More information

Practice. Newton s 3 Laws of Motion. Recall. Forces a push or pull acting on an object; a vector quantity measured in Newtons (kg m/s²)

Practice. Newton s 3 Laws of Motion. Recall. Forces a push or pull acting on an object; a vector quantity measured in Newtons (kg m/s²) Practice A car starts from rest and travels upwards along a straight road inclined at an angle of 5 from the horizontal. The length of the road is 450 m and the mass of the car is 800 kg. The speed of

More information

The ballistic pendulum

The ballistic pendulum (ta initials) first nae (print) last nae (print) brock id (ab17cd) (lab date) Experient 4 The ballistic pendulu In this Experient you will learn how to deterine the speed of a projectile as well as the

More information

Experiment 11. Moment of Inertia

Experiment 11. Moment of Inertia Experiment Moment of nertia A rigid body composed of concentric disks is constrained to rotate about its axis of symmetry. The moment of inertia is found by two methods and results are compared. n first

More information

13-Nov-2015 PHYS Rotational Inertia

13-Nov-2015 PHYS Rotational Inertia Objective Rotational Inertia To determine the rotational inertia of rigid bodies and to investigate its dependence on the distance to the rotation axis. Introduction Rotational Inertia, also known as Moment

More information

Acceleration due to Gravity

Acceleration due to Gravity Acceleration due to Gravity 1 Object To determine the acceleration due to gravity by different methods. 2 Apparatus Balance, ball bearing, clamps, electric timers, meter stick, paper strips, precision

More information

PHYSICS 221 SPRING 2014

PHYSICS 221 SPRING 2014 PHYSICS 221 SPRING 2014 EXAM 2: April 3, 2014 8:15-10:15pm Name (printed): Recitation Instructor: Section # INSTRUCTIONS: This exam contains 25 multiple-choice questions plus 2 extra credit questions,

More information

Newton s Second Law. Sample

Newton s Second Law. Sample Newton s Second Law Experiment 4 INTRODUCTION In your discussion of Newton s first law, you learned that when the sum of the forces acting on an object is zero, its velocity does not change. However, when

More information

III. Angular Momentum Conservation (Chap. 10) Rotation. We repeat Chap. 2-8 with rotatiing objects. Eqs. of motion. Energy.

III. Angular Momentum Conservation (Chap. 10) Rotation. We repeat Chap. 2-8 with rotatiing objects. Eqs. of motion. Energy. Chap. 10: Rotational Motion I. Rotational Kinematics II. Rotational Dynamics - Newton s Law for Rotation III. Angular Momentum Conservation (Chap. 10) 1 Toward Exam 3 Eqs. of motion o To study angular

More information

Pre-Lab Exercise Full Name:

Pre-Lab Exercise Full Name: L07 Rotational Motion and the Moment of Inertia 1 Pre-Lab Exercise Full Name: Lab Section: Hand this in at the beginning of the lab period. The grade for these exercises will be included in your lab grade

More information

Experiment P26: Rotational Inertia (Smart Pulley)

Experiment P26: Rotational Inertia (Smart Pulley) PASCO scientific Physics Lab Manual P26-1 Experiment P26: (Smart Pulley) Concept Time SW Interface Macintosh file Windows file rotational motion 45 m 500 or 700 P26 P26_ROTA.SWS EQUIPMENT NEEDED Interface

More information

Experiment 7: Newton s Second Law for Rotational Motion

Experiment 7: Newton s Second Law for Rotational Motion Chapter 9 Experiment 7: Newton s Second Law for Rotational Motion Isaac Newton (1642-1727) formalized the relationship between force and motion in his Principia (published in 1687) in which he proposed

More information

PHY 111L Activity 2 Introduction to Kinematics

PHY 111L Activity 2 Introduction to Kinematics PHY 111L Activity 2 Introduction to Kinematics Name: Section: ID #: Date: Lab Partners: TA initials: Objectives 1. Introduce the relationship between position, velocity, and acceleration 2. Investigate

More information

PHYSICS LAB. Newton's Law. Date: GRADE: PHYSICS DEPARTMENT JAMES MADISON UNIVERSITY

PHYSICS LAB. Newton's Law. Date: GRADE: PHYSICS DEPARTMENT JAMES MADISON UNIVERSITY PHYSICS LAB Newton's Law Printed Names: Signatures: Date: Lab Section: Instructor: GRADE: PHYSICS DEPARTMENT JAMES MADISON UNIVERSITY Revision August 2003 NEWTON S SECOND LAW Purpose: 1. To become familiar

More information

General Physics I Lab. M1 The Atwood Machine

General Physics I Lab. M1 The Atwood Machine Purpose General Physics I Lab In this experiment, you will learn the basic operation of computer interfacing and use it in an experimental study of Newton s second law. Equipment and components Science

More information

Rotational Motion. 1 Purpose. 2 Theory 2.1 Equation of Motion for a Rotating Rigid Body

Rotational Motion. 1 Purpose. 2 Theory 2.1 Equation of Motion for a Rotating Rigid Body Rotational Motion Equipment: Capstone, rotary motion sensor mounted on 80 cm rod and heavy duty bench clamp (PASCO ME-9472), string with loop at one end and small white bead at the other end (125 cm bead

More information

E X P E R I M E N T 11

E X P E R I M E N T 11 E X P E R I M E N T 11 Conservation of Angular Momentum Produced by the Physics Staff at Collin College Copyright Collin College Physics Department. All Rights Reserved. University Physics, Exp 11: Conservation

More information

Physics 101: Lecture 15 Torque, F=ma for rotation, and Equilibrium

Physics 101: Lecture 15 Torque, F=ma for rotation, and Equilibrium Physics 101: Lecture 15 Torque, F=ma for rotation, and Equilibrium Strike (Day 10) Prelectures, checkpoints, lectures continue with no change. Take-home quizzes this week. See Elaine Schulte s email. HW

More information

PHYSICS 221 SPRING EXAM 2: March 30, 2017; 8:15pm 10:15pm

PHYSICS 221 SPRING EXAM 2: March 30, 2017; 8:15pm 10:15pm PHYSICS 221 SPRING 2017 EXAM 2: March 30, 2017; 8:15pm 10:15pm Name (printed): Recitation Instructor: Section # Student ID# INSTRUCTIONS: This exam contains 25 multiple-choice questions plus 2 extra credit

More information

Our Final Exam will be held on Monday, December 7 at 8:00am!

Our Final Exam will be held on Monday, December 7 at 8:00am! Physics 2211 A/B Test form Name Fall 2015 Exam 4 Recitation Section (see back of test): 1) Print your name, test form number (above), and nine-digit student number in the section of the answer card labeled

More information

Static and Kinetic Friction

Static and Kinetic Friction Ryerson University - PCS 120 Introduction Static and Kinetic Friction In this lab we study the effect of friction on objects. We often refer to it as a frictional force yet it doesn t exactly behave as

More information

PHYSICS LAB Experiment 9 Fall 2004 THE TORSION PENDULUM

PHYSICS LAB Experiment 9 Fall 2004 THE TORSION PENDULUM PHYSICS 83 - LAB Experiment 9 Fall 004 THE TORSION PENDULUM In this experiment we will study the torsion constants of three different rods, a brass rod, a thin steel rod and a thick steel rod. We will

More information

Physics 101. Hour Exam 2 Spring Last Name: First Name Network-ID Discussion Section: Discussion TA Name:

Physics 101. Hour Exam 2 Spring Last Name: First Name Network-ID Discussion Section: Discussion TA Name: Last Name: First Name Network-ID Discussion Section: Discussion TA Name: Instructions Turn off your cell phone and put it away. This is a closed book exam. You have ninety (90) minutes to complete it.

More information

EXPERIMENT 2 Acceleration of Gravity

EXPERIMENT 2 Acceleration of Gravity Name Date: Course number: Laboratory Section: Partners Names: Last Revised on Februrary 3, 08 Grade: EXPERIENT Acceleration of Gravity. Pre-Laboratory Work [0 pts]. You have just completed the first part

More information

Force and Acceleration in Circular Motion

Force and Acceleration in Circular Motion Force and Acceleration in Circular Motion INTRODUCTION Acceleration is the time rate of change of velocity. Since velocity is a vector, it can change in two ways: its magnitude can change and its direction

More information

PHY 123 Lab 9 Simple Harmonic Motion

PHY 123 Lab 9 Simple Harmonic Motion PHY 123 Lab 9 Simple Harmonic Motion (updated 11/17/16) The purpose of this lab is to study simple harmonic motion of a system consisting of a mass attached to a spring. You will establish the relationship

More information

Final Exam April 30, 2013

Final Exam April 30, 2013 Final Exam Instructions: You have 120 minutes to complete this exam. This is a closed-book, closed-notes exam. You are allowed to use a calculator during the exam. Usage of mobile phones and other electronic

More information

1 M62 M62.1 CONSERVATION OF ANGULAR MOMENTUM FOR AN INELASTIC COLLISION

1 M62 M62.1 CONSERVATION OF ANGULAR MOMENTUM FOR AN INELASTIC COLLISION 1 M62 M62.1 CONSERVATION OF ANGULAR MOMENTUM FOR AN INELASTIC COLLISION PRELAB: Before coming to the lab, you must write the Object and Theory sections of your lab report and include the Data Tables. You

More information

PHYSICS 221 Fall 2016 EXAM 2: November 02, :15pm 10:15pm. Name (printed): Recitation Instructor: Section #:

PHYSICS 221 Fall 2016 EXAM 2: November 02, :15pm 10:15pm. Name (printed): Recitation Instructor: Section #: PHYSICS 221 Fall 2016 EXAM 2: November 02, 2016 8:15pm 10:15pm Name (printed): Recitation Instructor: Section #: INSTRUCTIONS: This exam contains 25 multiple-choice questions, plus 2 extra-credit questions,

More information

16. Rotational Dynamics

16. Rotational Dynamics 6. Rotational Dynamics A Overview In this unit we will address examples that combine both translational and rotational motion. We will find that we will need both Newton s second law and the rotational

More information

Experiment #9 Comments, Thoughts and Suggestions

Experiment #9 Comments, Thoughts and Suggestions Experiment #9 Comments, Thoughts and Suggestions The purpose of this paper is to provide you with some information which may be useful for solving the pre-lab questions and performing the lab. I will attempt

More information

Physics 111. Tuesday, November 2, Rotational Dynamics Torque Angular Momentum Rotational Kinetic Energy

Physics 111. Tuesday, November 2, Rotational Dynamics Torque Angular Momentum Rotational Kinetic Energy ics Tuesday, ember 2, 2002 Ch 11: Rotational Dynamics Torque Angular Momentum Rotational Kinetic Energy Announcements Wednesday, 8-9 pm in NSC 118/119 Sunday, 6:30-8 pm in CCLIR 468 Announcements This

More information

Forces and Newton s Second Law

Forces and Newton s Second Law Forces and Newton s Second Law Goals and Introduction Newton s laws of motion describe several possible effects of forces acting upon objects. In particular, Newton s second law of motion says that when

More information

Exam 3 April 16, 2014

Exam 3 April 16, 2014 Exam 3 Instructions: You have 60 minutes to complete this exam. This is a closed-book, closed-notes exam. You are allowed to use a calculator during the exam. Usage of mobile phones and other electronic

More information

Physics Kinematics, Projectile Motion, Free-Body Diagrams, and Rotational Motion

Physics Kinematics, Projectile Motion, Free-Body Diagrams, and Rotational Motion Physics Kinematics, Projectile Motion, Free-Body Diagrams, and Rotational Motion Kinematics and Projectile Motion Problem Solving Steps 1. Read and Re-Read the whole problem carefully before trying to

More information

PHYSICS LAB Experiment 4 Fall 2004 ATWOOD S MACHINE: NEWTON S SECOND LAW

PHYSICS LAB Experiment 4 Fall 2004 ATWOOD S MACHINE: NEWTON S SECOND LAW PHYSICS 83 - LAB Experiment 4 Fall 004 ATWOOD S MACHINE: NEWTON S SECOND LAW th In this experiment we will use a machine, used by George Atwood in the 8 century, to measure the gravitational acceleration,

More information

Big Idea 4: Interactions between systems can result in changes in those systems. Essential Knowledge 4.D.1: Torque, angular velocity, angular

Big Idea 4: Interactions between systems can result in changes in those systems. Essential Knowledge 4.D.1: Torque, angular velocity, angular Unit 7: Rotational Motion (angular kinematics, dynamics, momentum & energy) Name: Big Idea 3: The interactions of an object with other objects can be described by forces. Essential Knowledge 3.F.1: Only

More information

LAB 4: FORCE AND MOTION

LAB 4: FORCE AND MOTION Lab 4 - Force & Motion 37 Name Date Partners LAB 4: FORCE AND MOTION A vulgar Mechanik can practice what he has been taught or seen done, but if he is in an error he knows not how to find it out and correct

More information

Updated 2013 (Mathematica Version) M1.1. Lab M1: The Simple Pendulum

Updated 2013 (Mathematica Version) M1.1. Lab M1: The Simple Pendulum Updated 2013 (Mathematica Version) M1.1 Introduction. Lab M1: The Simple Pendulum The simple pendulum is a favorite introductory exercise because Galileo's experiments on pendulums in the early 1600s are

More information

Chapter 6, Problem 18. Agenda. Rotational Inertia. Rotational Inertia. Calculating Moment of Inertia. Example: Hoop vs.

Chapter 6, Problem 18. Agenda. Rotational Inertia. Rotational Inertia. Calculating Moment of Inertia. Example: Hoop vs. Agenda Today: Homework quiz, moment of inertia and torque Thursday: Statics problems revisited, rolling motion Reading: Start Chapter 8 in the reading Have to cancel office hours today: will have extra

More information

Rotational Inertia (approximately 2 hr) (11/23/15)

Rotational Inertia (approximately 2 hr) (11/23/15) Inertia (approximately 2 hr) (11/23/15) Introduction In the case of linear motion, a non-zero net force will result in linear acceleration in accordance with Newton s 2 nd Law, F=ma. The moving object

More information

Newton s Second Law. Newton s Second Law of Motion describes the results of a net (non-zero) force F acting on a body of mass m.

Newton s Second Law. Newton s Second Law of Motion describes the results of a net (non-zero) force F acting on a body of mass m. Newton s Second Law Newton s Second Law of Motion describes the results of a net (non-zero) force F acting on a body of mass m. F net = ma (1) It should come as no surprise that this force produces an

More information

Conservation of Mechanical Energy Activity Purpose

Conservation of Mechanical Energy Activity Purpose Conservation of Mechanical Energy Activity Purpose During the lab, students will become familiar with solving a problem involving the conservation of potential and kinetic energy. A cart is attached to

More information

STUDY GUIDE 4: Equilibrium, Angular Kinematics, and Dynamics

STUDY GUIDE 4: Equilibrium, Angular Kinematics, and Dynamics PH 1110 Term C11 STUDY GUIDE 4: Equilibrium, Angular Kinematics, and Dynamics Objectives 25. Define torque. Solve problems involving objects in static equilibrium. 26. Define angular displacement, angular

More information

Phys 106 Practice Problems Common Quiz 1 Spring 2003

Phys 106 Practice Problems Common Quiz 1 Spring 2003 Phys 106 Practice Problems Common Quiz 1 Spring 2003 1. For a wheel spinning with constant angular acceleration on an axis through its center, the ratio of the speed of a point on the rim to the speed

More information

Motion on a linear air track

Motion on a linear air track Motion on a linear air track Introduction During the early part of the 17 th century, Galileo experimentally examined the concept of acceleration. One of his goals was to learn more about freely falling

More information

PHYSICS LAB Experiment 6 Fall 2004 WORK AND ENERGY GRAVITY

PHYSICS LAB Experiment 6 Fall 2004 WORK AND ENERGY GRAVITY PHYSICS 183 - LAB Experiment 6 Fall 004 WORK AND ENERGY GRAVITY In this experiment we will study the effects of the work-energy theorem, which states that the change in the kinetic energy (1/Mv ) of an

More information

8.012 Physics I: Classical Mechanics Fall 2008

8.012 Physics I: Classical Mechanics Fall 2008 MIT OpenCourseWare http://ocw.mit.edu 8.012 Physics I: Classical Mechanics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. MASSACHUSETTS INSTITUTE

More information

It will be most difficult for the ant to adhere to the wheel as it revolves past which of the four points? A) I B) II C) III D) IV

It will be most difficult for the ant to adhere to the wheel as it revolves past which of the four points? A) I B) II C) III D) IV AP Physics 1 Lesson 16 Homework Newton s First and Second Law of Rotational Motion Outcomes Define rotational inertia, torque, and center of gravity. State and explain Newton s first Law of Motion as it

More information

Uniformly Accelerated Motion

Uniformly Accelerated Motion Uniformly Accelerated Motion 2-1 Uniformly Accelerated Motion INTRODUCTION All objects on the earth s surface are being accelerated toward the center of the earth at a rate of 9.81 m/s 2. 1 This means

More information

Laboratory Exercise. Newton s Second Law

Laboratory Exercise. Newton s Second Law Laboratory Exercise Newton s Second Law INTRODUCTION Newton s first law was concerned with the property of objects that resists changes in motion, inertia. Balanced forces were the focus of Newton s first

More information

Motion with Constant Acceleration

Motion with Constant Acceleration Motion with Constant Acceleration INTRODUCTION Newton s second law describes the acceleration of an object due to an applied net force. In this experiment you will use the ultrasonic motion detector to

More information

Name Date: Course number: MAKE SURE TA & TI STAMPS EVERY PAGE BEFORE YOU START. Grade: EXPERIMENT 4

Name Date: Course number: MAKE SURE TA & TI STAMPS EVERY PAGE BEFORE YOU START. Grade: EXPERIMENT 4 Laboratory Section: Last Revised on June 18, 2018 Partners Names: Grade: EXPERIMENT 4 Moment of Inertia & Oscillations 0 Pre-Laboratory Work [20 pts] 1 a) In Section 31, describe briefly the steps you

More information

PHYSICS 111 SPRING EXAM 2: March 6, 2018; 8:15-9:45 pm

PHYSICS 111 SPRING EXAM 2: March 6, 2018; 8:15-9:45 pm PHYSICS 111 SPRING 2018 EXAM 2: March 6, 2018; 8:15-9:45 pm Name (printed): Recitation Instructor: Section # INSTRUCTIONS: This exam contains 20 multiple-choice questions plus 1 extra credit question,

More information

Rotation. Rotational Variables

Rotation. Rotational Variables Rotation Rigid Bodies Rotation variables Constant angular acceleration Rotational KE Rotational Inertia Rotational Variables Rotation of a rigid body About a fixed rotation axis. Rigid Body an object that

More information

Handout 7: Torque, angular momentum, rotational kinetic energy and rolling motion. Torque and angular momentum

Handout 7: Torque, angular momentum, rotational kinetic energy and rolling motion. Torque and angular momentum Handout 7: Torque, angular momentum, rotational kinetic energy and rolling motion Torque and angular momentum In Figure, in order to turn a rod about a fixed hinge at one end, a force F is applied at a

More information

LAB 9: EQUILIBRIUM OF NON-PARALLEL FORCES

LAB 9: EQUILIBRIUM OF NON-PARALLEL FORCES Name Date artners LAB 9: EQUILIBRIUM O NON-ARALLEL ORCES 145 OBJECTIVES OVERVIEW To study the components of forces To examine forces in static equilibrium To examine torques To study the conditions for

More information

Lab 4: Projectile Motion

Lab 4: Projectile Motion 59 Name Date Partners OVEVIEW Lab 4: Projectile Motion We learn in our study of kinematics that two-dimensional motion is a straightforward extension of one-dimensional motion. Projectile motion under

More information

Human Arm. 1 Purpose. 2 Theory. 2.1 Equation of Motion for a Rotating Rigid Body

Human Arm. 1 Purpose. 2 Theory. 2.1 Equation of Motion for a Rotating Rigid Body Human Arm Equipment: Capstone, Human Arm Model, 45 cm rod, sensor mounting clamp, sensor mounting studs, 2 cord locks, non elastic cord, elastic cord, two blue pasport force sensors, large table clamps,

More information

8.012 Physics I: Classical Mechanics Fall 2008

8.012 Physics I: Classical Mechanics Fall 2008 MIT OpenCourseWare http://ocw.mit.edu 8.012 Physics I: Classical Mechanics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. MASSACHUSETTS INSTITUTE

More information

College Physics I Laboratory Angular Momentum

College Physics I Laboratory Angular Momentum College Physics I Laboratory Angular Momentum Purpose PHSX 206N To investigate conservation of angular momentum by directly measuring the moment of inertia and angular velocities for initial and final

More information

End-of-Chapter Exercises

End-of-Chapter Exercises End-of-Chapter Exercises Exercises 1 12 are conceptual questions that are designed to see if you have understood the main concepts of the chapter. 1. Figure 11.21 shows four different cases involving a

More information

= o + t = ot + ½ t 2 = o + 2

= o + t = ot + ½ t 2 = o + 2 Chapters 8-9 Rotational Kinematics and Dynamics Rotational motion Rotational motion refers to the motion of an object or system that spins about an axis. The axis of rotation is the line about which the

More information

Rotational Equilibrium

Rotational Equilibrium Rotational Equilibrium 6-1 Rotational Equilibrium INTRODUCTION Have you ever tried to pull a stubborn nail out of a board or develop your forearm muscles by lifting weights? Both these activities involve

More information

PHYSICS 149: Lecture 21

PHYSICS 149: Lecture 21 PHYSICS 149: Lecture 21 Chapter 8: Torque and Angular Momentum 8.2 Torque 8.4 Equilibrium Revisited 8.8 Angular Momentum Lecture 21 Purdue University, Physics 149 1 Midterm Exam 2 Wednesday, April 6, 6:30

More information

第 1 頁, 共 7 頁 Chap10 1. Test Bank, Question 3 One revolution per minute is about: 0.0524 rad/s 0.105 rad/s 0.95 rad/s 1.57 rad/s 6.28 rad/s 2. *Chapter 10, Problem 8 The angular acceleration of a wheel

More information