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Rotational Dynamics in the Playground

William Liu and Tuong Phung

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Goals and Important Concepts

  • Merry-go-round + Gravity Spinner Bowl
    • Conservation of Angular Momentum
    • Angular Acceleration and Velocity
    • Centripetal Force and Friction
    • And perhaps many more…
  • Important topics in most introductory physics courses in high school!
  • Can physically replicate and experience many of the common problems (that can’t be easily or safely replicated) students see in textbooks through movement here
    • Will develop a deeper and better intuition of the concepts

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Gravity Spinner Bowl

Mini

Merry-go-round

(“broken”, but we still managed to use it!)

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Conservation of Angular Momentum

  • Common textbook example: the figure skater

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  • Students can experience this on the mini merry-go-round

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  • Spin on it with their arms stretched out, and then wrap their arms in tightly

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What Students Will Experience

  • When students have their arms extended, they have a higher rotational inertia, so they will experience a lower angular velocity

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  • When students bring their arms in, they will decrease their rotational inertia, so they will increase their angular velocity proportionally and spin faster

  • Lighter students might notice they experience a lesser change, due to the mass factor in momentum

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Relating Linear and Angular Variables

  • Linear kinematic variables (i.e. position, velocity, and acceleration) are related to their corresponding angular variables (i.e. angular position, angular velocity, and angular acceleration) by multiplying by the radius - often the first topic taught in circular motion, but usually only with abstract formulas

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  • Students can experience this by moving towards and away from the center of the gravity spinner bowl while it is spinning

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What Students Will Experience

  • As they move towards the rim of the gravity spinner bowl, they will experience increased linear speed/acceleration

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  • When they’re at the center of the bowl, they won’t experience any linear speed/acceleration or change in linear position

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Centripetal Force + Friction

  • Common textbook example: the carnival rotor, car on a sharp turn, car on a banked ramp
  • Students can replicate it on the gravity bowl
    • At the playground we visited, the spinning bowl was small as it was designed for really young kids
    • We used a backpack to act as the student
  • Stay in the gravity bowl, see what the required rate of spinning is to avoid sliding down due to friction or sliding up due to centripetal force
  • Manually do this and collect data for later calculations!

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What Students Will Experience

  • If the bowl is spinning quickly enough, then the student may slide outwards

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  • If the bowl is not spinning or is spinning too slowly, then the student may slide inwards

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  • The results are dependent on the friction between the student and the surface of the bowl

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Other Ideas We Had

Rock Climbing (Physiology)

Anatomy and physiology of rock climbing

Hyperbolic trigonometry and catenary curves

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Swings and simple harmonic motion

Materials science of playground surfaces

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Slides, forces, and friction (linear kinematics)

3D geometry and polyhedra

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References (for Images)