the Public Broadcasting Service
the Show of Force Productions
This video-based resource examines center of mass, a concept that plays an important role in balance. The video explores the relationship between torque and center of mass for a circus acrobat. The circus act involves two people: the bottom acrobat moves about the circus ring supporting the top acrobat, who balances on pointe upon her partner's head. When the top acrobat's center of mass is not over the point of support, a torque results. Background information explains how to calculate torque (in terms of a simpler see-saw system). Also included are tips on how to incorporate the video into instruction, discussion questions, and accompanying classroom activities.
This resource was developed in conjunction with the PBS series Circus. See Related Materials for a link to the full set of 8 Circus Physics video-based lessons.
9-12: 2B/H3. Mathematics provides a precise language to describe objects and events and the relationships among them. In addition, mathematics provides tools for solving problems, analyzing data, and making logical arguments.
4. The Physical Setting
9-12: 4F/H1. The change in motion (direction or speed) of an object is proportional to the applied force and inversely proportional to the mass.
9-12: 4F/H2. All motion is relative to whatever frame of reference is chosen, for there is no motionless frame from which to judge all motion.
9-12: 4F/H4. Whenever one thing exerts a force on another, an equal amount of force is exerted back on it.
9-12: 4F/H8. Any object maintains a constant speed and direction of motion unless an unbalanced outside force acts on it.
Next Generation Science Standards
Motion and Stability: Forces and Interactions (HS-PS2)
Students who demonstrate understanding can: (9-12)
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. (HS-PS2-1)
Disciplinary Core Ideas (K-12)
Forces and Motion (PS2.A)
The motion of an object is determined by the sum of the forces acting on it; if the total force on the object is not zero, its motion will change. The greater the mass of the object, the greater the force needed to achieve the same change in motion. For any given object, a larger force causes a larger change in motion. (6-8)
Newton's second law accurately predicts changes in the motion of macroscopic objects. (9-12)
Relationship Between Energy and Forces (PS3.C)
When two objects interact, each one exerts a force on the other that can cause energy to be transferred to or from the object. (6-8)
NGSS Science and Engineering Practices (K-12)
Using Mathematics and Computational Thinking (5-12)
Mathematical and computational thinking at the 9–12 level builds on K–8 and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data. Simple computational simulations are created and used based on mathematical models of basic assumptions. (9-12)
Use mathematical representations of phenomena or design solutions to support and revise explanations. (9-12)
Common Core State Standards for Mathematics Alignments
High School — Algebra (9-12)
Seeing Structure in Expressions (9-12)
A-SSE.1.a Interpret parts of an expression, such as terms, factors, and coefficients.
A-SSE.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.
A-SSE.2 Use the structure of an expression to identify ways to rewrite it.
Creating Equations? (9-12)
A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
Show of Force Productions. Circus Physics: Center of Mass. Arlington: Public Broadcasting Service, 2010. http://www.pbs.org/opb/circus/classroom/circus-physics/center-mass/ (accessed 17 September 2014).
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