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Teacher Notes
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Teacher Notes Rotational Motion and Angular MomentumInquiry Lab Kit for AP® Physics 1Materials Included In KitPulley cord, 13.7 meters Additional Materials Required(for each lab group) Safety PrecautionsWear safety glasses while performing this experiment. DisposalAll materials may be saved and stored for future use. Lab Hints
Teacher Tips
Further ExtensionsOpportunities for Inquiry Correlation to Next Generation Science Standards (NGSS)†Science & Engineering PracticesDeveloping and using modelsPlanning and carrying out investigations Analyzing and interpreting data Using mathematics and computational thinking Constructing explanations and designing solutions Disciplinary Core IdeasHS-PS2.A: Forces and MotionHS-PS3.A: Definitions of Energy HS-PS3.B: Conservation of Energy and Energy Transfer Crosscutting ConceptsPatternsCause and effect Scale, proportion, and quantity Energy and matter Performance ExpectationsHS-PS2-1. Analyze data to support the claim that Newton’s second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration. Answers to Prelab Questions
Sample DataIntroductory Activity {13791_Data_Table_1}
Calculations for Wheel 1 a = 2d/t2{13791_Data_Equation_1}
a = 0.246 m/s2
{13791_Data_Equation_2}
{13791_Data_Equation_3}
α = 14.1 rad/s2T = FT x r = I x α {13791_Data_Equation_4}
{13791_Data_Equation_5}
{13791_Data_Equation_6}
{13791_Data_Equation_7}
I = 1.19 x 10–4 kg∙m2ΔL = IαΔt ΔL = (1.19 x 10–4 kg∙m2)(14.1 rad/s2)(2.75 s) ΔL = 0.00460 kg∙m2/s ω = ωo + αt ω = 0 rad/s + (14.1 rad/s2)(2.75 s) ω = 38.6 rad/s θ = θo + ωot + ½αt2 θ = ½αt2 θ = ½(14.1 rad/s2)(2.75 s)2 θ = 53.1 rad Guided-Inquiry Design and Procedure {13791_Data_Table_1}
Percent Error of Fall TimePercent Error = |Experimental – Theoretical|/Theoretical x 100 For Wheel 1: Percent Error = |1.85 s – 2.00 s|/2.00 s x 100 Overall, the experiment was successful. Each wheel had fall times that were close to the required 2.00 seconds. Random errors due to timing may have contributed to the larger percent errors of the larger wheels. The masses required for the larger wheels were small washers and it was difficult to determine when the washers hit the floor. It was easier to hear the masses for the smaller wheels because larger washers were used. Photogates with automated timekeeping could be used to lower the number of timing errors due to human reaction time. Answers to QuestionsGuided-Inquiry Design and Procedure
{13791_Data_Equation_8}
{13791_Data_Equation_9}
a = 0.465 m/s2T = FT x r = I x α {13791_Data_Equation_10}
{13791_Data_Equation_11}
{13791_Data_Equation_12}
{13791_Data_Equation_13}
mh = 0.0198 kg = 19.8 g
ReferencesAP Physics 1: Algebra-Based and Physics 2: Algebra-Based Curriculum Framework; The College Board: New York, NY, 2014. Recommended Products
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Student Pages
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Student PagesRotational Motion and Angular MomentumIntroductionWhat would be more difficult to stop: a small, solid wheel spinning fast or a Ferris wheel spinning slowly? What equations and variables describe the motion and properties of these spinning objects? Discover the relationship between rotational motion and angular momentum. Concepts
BackgroundA rigid body sitting on a frictionless surface follows Newton’s second law of motion. If a constant force, F, is applied (see Figure 1), and the body is initially at rest, the equations of motion are as follows for acceleration, velocity and distance where m is the total mass of the rigid body: {13791_Background_Figure_1}
{13791_Background_Equation_1}
{13791_Background_Equation_2}
{13791_Background_Equation_3}
A rigid body that rotates around a fixed axis has equivalent rotational equations to the translational (linear) equations above. The rotational equivalents are: angular displacement, θ, measured in radians (rad); angular velocity, ω, measured in rad/sec; and angular acceleration, α, measured in rad/s2. Rotational motion with constant angular acceleration can be described by the following equations:
{13791_Background_Equation_4}
{13791_Background_Equation_5}
{13791_Background_Equation_6}
Rotational motion is related to linear motion by considering how far the point of interest is from the axis of rotation. This distance is typically the radius, r, of the object.
{13791_Background_Equation_7}
{13791_Background_Equation_8}
{13791_Background_Equation_9}
For a rotating object, the equivalent to mass is called the moment of inertia, I. For a symmetrical disk of uniform density and a radius of R (see Figure 2):
{13791_Background_Equation_10}
{13791_Background_Figure_2}
To cause rotation, a force must be applied at a radial distance, r, from the fixed, rotational axis. Torque, T, is the rotational equivalent to force in a linear system and is equal to the product of the radial distance from the center to where the force is applied, the magnitude of the force, and the angle between the two. In the case of rotating objects, the angle between the force and radial distance is 90°. See Figure 2 and Equation 11:
{13791_Background_Equation_11}
Because torque is an external force on the disk, it influences the angular acceleration of the disk:
{13791_Background_Equation_12}
If the external torque were to be removed from the disk, it would continue to rotate. Like a box sliding across the floor, both objects have momentum. For the disk, this is called angular momentum and is the product of the angular velocity and moment of inertia of the object. Angular momentum is measured in kg∙m2/s.
{13791_Background_Equation_13}
If the disk starts out at rest, the change in angular momentum can be calculated by multiplying the net torque and the duration of time the torque is applied to the disk.
{13791_Background_Equation_14}
The sign convention for rotational motion, including torque, angular acceleration and angular momentum, is based on the direction of the rotation. If the rotation is counterclockwise, the value is positive. If the rotation is clockwise, it is a negative value.
Experiment OverviewThe purpose of this advanced inquiry investigation is to verify the connection between Newton’s second laws of linear and rotational motion. The lab begins with an Introductory Activity to determine the moment of inertia for a solid disk having four pulley arrangements. Then, the Guided-Inquiry Design and Procedure section presents a challenge to use the data from the Introductory Activity to calculate, and then verify, the correct mass to attach to each flywheel, so that it takes 2.00 seconds to fall from the bench height to the floor. MaterialsBalance, 0.01-g precision Prelab Questions
Safety PrecautionsStudents should wear safety glasses while performing this experiment. ProcedureIntroductory Activity Falling Mass and Rotational Motion
Analyze the Results Present the data collected in the Introductory Activity in an appropriate table. Calculate the following for each radii of the wheel: acceleration of the free falling mass, angular acceleration of the the wheel, moment of inertia of the wheel, and angular momentum of the wheel. Remember to consider the sign of torque, angular acceleration and angular momentum based on the direction of rotation. Also calculate the final angular velocity, ω, and the angular displacement, θ, of the wheel at each radius. Guided-Inquiry Design and Procedure
Analyze the Results Present the actual hanging mass values and free fall times in an appropriate data table. Calculate the following for each radii of the wheel: acceleration of the free falling mass, angular acceleration of the wheel and the change in angular momentum of the wheel. Remember to consider the sign of torque, angular acceleration and angular momentum based on the direction of rotation. Calculate the percent error in the fall times for each wheel and discuss the reliability of the experiment and methods to improve the experiment. Student Worksheet PDF |