the Public Broadcasting Service
the Show of Force Productions
This video-based resource examines conservation of angular momentum through the motion of an acrobat doing aerial flips. It explores how a tucked position decreases the acrobat's moment of inertia, resulting in increased rotational velocity. To slow his rotation, he extends his legs. Through the acrobat's motion, the video illustrates how angular momentum is conserved for a body in flight. Supplementary materials help students integrate concepts to perform calculations relating to angular momentum and moment of inertia.
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/H8. Any object maintains a constant speed and direction of motion unless an unbalanced outside force acts on it.
Next Generation Science Standards
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)
Momentum is defined for a particular frame of reference; it is the mass times the velocity of the object. (9-12)
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
Standards for Mathematical Practice (K-12)
MP.2 Reason abstractly and quantitatively.
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.
Creating Equations? (9-12)
A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
High School — Functions (9-12)
Linear, Quadratic, and Exponential Models? (9-12)
F-LE.1.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context.
Circus Physics: Conservation of Angular Momentum. (2010). Retrieved February 24, 2017, from Public Broadcasting Service: http://www.pbslearningmedia.org/resource/1d1f951e-5af8-4e43-b63a-19d55aa60780/1d1f951e-5af8-4e43-b63a-19d55aa60780/
Show of Force Productions. Circus Physics: Conservation of Angular Momentum. Arlington: Public Broadcasting Service, 2010. http://www.pbslearningmedia.org/resource/1d1f951e-5af8-4e43-b63a-19d55aa60780/1d1f951e-5af8-4e43-b63a-19d55aa60780/ (accessed 24 February 2017).
Circus Physics: Conservation of Angular Momentum. Arlington: Public Broadcasting Service, 2010. Show of Force Productions. 24 Feb. 2017 <http://www.pbslearningmedia.org/resource/1d1f951e-5af8-4e43-b63a-19d55aa60780/1d1f951e-5af8-4e43-b63a-19d55aa60780/>.
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