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AP Physics 1 Investigation 7:
Rotational Motion
What physical characteristics of an object affect
the translational speed of the object after it has
rolled to the bottom of an incline?
Central Challenge
This investigation introduces students to concepts of rotational motion as they
analyze how characteristics of objects such as mass, radius, and shape affect
the linear speeds of those objects at the bottom of a ramp. This lab provides
instructions for both qualitative and quantitative investiga

Transcript

141
AP P HY S I C S 1 I NVE S T I GAT I ON S
AP Physics 1 Investigation 7:
Rotational Motion
What physical characteristics of an object affect the translational speed of the object after it has rolled to the bottom of an incline?
Central Challenge
This investigation introduces students to concepts of rotational motion as they analyze how characteristics of objects such as mass, radius, and shape affect the linear speeds of those objects at the bottom of a ramp. This lab provides instructions for both qualitative and quantitative investigations in rotational motion, giving you the option of choosing which type of investigation is best for your students. If time permits, you might choose to have them complete both investigations.
Background
Without friction, an object at the top of an incline would slide down the incline without rolling, resulting in only linear (or translational) motion. A friction force exerts a torque on the object, allowing it to roll down the incline. Basic kinematic equations already familiar to students can describe the linear (or translational) motion of the center of mass of the object as it changes position, but rotational motion equations must be incorporated to describe the rotational motion of each object as it rolls without slipping down the ramp. Additionally, the way in which an object rotates depends upon the rotational inertia of the object. Although students will not calculate rotational inertia in this course, they will use the concept of rotational inertia in calculations of quantities such as torque and rotational kinetic energy. This lab helps to provide a conceptual understanding of the physics properties of an object that deﬁne the object’s rotational inertia.
Real-World Application
It is not difﬁcult for students to visualize numerous everyday objects that rotate. Understanding how an object’s properties impact rotational motion allows students to critically examine designs used for rotating objects. For example, bicycle racers will choose wheel designs that have properties that can enhance their racing performance. Wheels that are fairly uniform from hub to rim with light rims have low rotational inertia, so they start quickly for a short race. However, bicycle wheels with light spokes and heavier rims have higher rotational inertia, which make the bicycle more difﬁcult to start, but once these wheels are turning they are less inﬂuenced by other forces and require more torque to stop — better for a long race or for stability on a rough terrain.
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© 2015 The College Board
A P P H Y S I C S 1 I N V E S T I G A T I O N S
142AP Physics 1 Investigation 7
Another common example is a spinning skater. The skater can exert a torque by pushing on the ice with an extended toe. Once the skater starts rotating, bringing legs and arms in close to the spin axis causes a faster spin. Extending the arms or a leg slows the spinner down to a stop. With arms and legs spinning close to the body (and close to the spin axis), the skater has a lower effective radius of spin and lower rotational inertia. Since angular momentum is the product of rotational inertia and angular speed, angular momentum is conserved when that product remains constant. If no external torque is exerted on the skater, reducing the rotational inertia results in a faster angular speed (and faster spin), and extending to increase the rotational inertia results in lower angular speed.
Inquiry Overview
Students are provided with materials to setup a ramp and objects of various shapes, sizes, and masses to design an experiment to test how objects rotate as they roll down a ramp. If students are provided with a large assortment of objects and options to create the inclined plane, they are given more opportunity for guided inquiry that approaches open inquiry, which is recommended. Students should be given latitude to make decisions about which objects to use, how many trials are adequate, how to make measurements to determine the speed of the object at the bottom of the ramp, and how to analyze their results. Students should be provided with the opportunity prior to actual lab time to meet in groups to design their lab procedure (even though some directions are provided). It adds to the inquiry process for students to report out their procedural plans to the other groups in order to gain feedback about oversights or gain suggestions prior to actually conducting the experiment. This can also happen postlab, giving students the opportunity to engage in critical discussions with the other groups.Initially, student groups will make qualitative predictions about how object shape, size, and mass will affect the speed of the object as it reaches the bottom of the ramp. These predictions will be discussed and compared in small student groups and recorded. Then students will run the trials and make qualitative observations. Finally, students will design methods to make measurements of the speeds of the objects at the bottom of the ramp to compare to their predictions and observations.
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© 2015 The College Board
143
AP P HY S I C S 1 I NVE S T I GAT I ON S
Rotational Motion
Connections to the AP Physics 1 Curriculum Framework
Big Idea 3
The interactions of an object with other objects can be described by forces.
Enduring UnderstandingLearning Objectives
3
.A
All forces share certain common characteristics when considered by observers in inertial reference frames.
3
.A.
1
.
1
The student is able to express the motion of an object using narrative, mathematical, and graphical representations. (Science Practices
1
.
5
,
2
.
1
, and
2
.
2
)
3
.A.
1
.
2
The student is able to design an experimental investigation of the motion of an object. (Science Practice
4
.
2
)
3
.A.
1
.
3
The student is able to analyze experimental data describing the motion of an object and is able to express the results of the analysis using narrative, mathematical, and graphical representations. (Science Practice
5
.
1
)
Big Idea 4
Interactions between systems can result in changes in those systems.
Enduring UnderstandingLearning Objectives
4
.C
Interactions with other objects or systems can change the total energy of a system.
4
.C.
1
.
1
The student is able to calculate the total energy of a system and justify the mathematical routines used in the calculation of component types of energy within the system whose sum is the total energy. (Science Practices
1
.
4
,
2
.
1
, and
2
.
2
)
Big Idea 5
Changes that occur as a result of interactions are constrained by conservation laws.
Enduring UnderstandingLearning Objectives
5
.E
The angular momentum of a system is conserved.
5
.E.
2
.
1
The student is able to describe or calculate the angular momentum and rotational inertia of a system in terms of the locations and velocities of objects that make up the system. Students are expected to do qualitative reasoning with compound objects. Students are expected to do calculations with a ﬁxed set of extended objects and point masses. (Science Practice
2
.
2
)
[
NOTE
:
In addition to those listed in the learning objectives above, Science Practice 4.3 is also addressed in this investigation.]
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© 2015 The College Board
A P P H Y S I C S 1 I N V E S T I G A T I O N S
144AP Physics 1 Investigation 7
Skills and Practices Taught/Emphasized in This Investigation
Science PracticesActivities
1
.
4
The student can
use representations and models
to analyze situations or solve problems qualitatively and quantitatively.Students include diagrams of objects and experimental setups in order to describe procedures, and they provide qualitative explanations and/or mathematical calculations as part of their analysis.
1
.
5
The student can
re-express key elements of natural phenomena across multiple representations
in the domain. Students support work with written observations of the objects’ motion as part of the analysis, and they include diagrams as part of background and analysis. If the quantitative method is used, students also express the motion with equations and calculations.
2
.
1
The student can justify
the selection of a mathematical routine
to solve problems.If the quantitative method is selected, students use equations and calculations to support predictions about which objects move with greater translational speed at the bottom of the ramp.
2
.
2
The student can
apply mathematical routines
to quantities that describe natural phenomena.Students apply selected mathematical routines to the calculations of speed if the qualitative method is selected.
4
.
2
The student can
design a plan
for collecting data to answer a particular scientiﬁc question.Students make decisions about which objects to test, how to design ramps, how to measure translational speed at the bottom of the ramp, and how to appropriately analyze the data.
4
.
3
The student can
collect data
to answer a particular scientiﬁc question.Students use observations in the qualitative method or numerical measurements in the quantitative method.
5
.
1
The student can
analyze data
to identify patterns or relationships.Students decide what methods will be used to analyze the data, such as graphing speed at the bottom of the ramp as a function of object radius for objects of the same mass and shape.
[
NOTE
:
Students should be keeping artifacts (lab notebook, portfolio, etc.) that may be used as evidence when trying to get lab credit at some institutions.]
Equipment and Materials
Per lab group (three to four students):
▶
Objects of different shapes, masses, and diameters (that can roll down an incline)
▶
Inclined plane or inclined grooved track (with sufﬁcient coefﬁcient of friction that chosen objects only roll and do not slide)
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© 2015 The College Board

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