Mechanics Week 14
Week 14 - Angular Motion & Simple Harmonic Motion
In Class Activity Plan (Word, Pdf)
Week 14: Angular Motion & Simple Harmonic Motion
25 min Whiteboard - Satellite Centripetal Ranking Problem (Word, Pdf)
PURPOSE: Practice modeling centripetal acceleration situation.
Lots of options here; probably want to give one as homework.
20 min Board Meeting
PURPOSE: Build consensus around modeling centripetal acceleration situation.
Goals:
Centripetal force is just the net force towards the center
Need to attend to the radius of the circular path
Additional resources which could be used:
Ferris Wheel Centripetal Force (Word, Pdf)
Centripetal Force Ranking (Word, Pdf)
Circular Motion Problems (Word, Pdf)
20 min Whiteboard - Ladybug Revolution part 1
PURPOSE: Investigate rotational motion; introduce rotational analogs to translational kinematics
Direct students to PhET simulation – Ladybug Revolution: http://phet.colorado.edu/en/simulation/rotation
Give students 10 minutes to explore.
Summarize what you have learned on whiteboard.
10 min Board Meeting
PURPOSE: Share what was learned from investigation of simulation
20 min Whiteboard - Ladybug Revolution part 2
PURPOSE: Develop models for constant rotational motion from graphs of rotational motion.
Directions: Return to the Ladybug Revolution simulation. Use the second tab which shows graphs, use radians.
Answer: What have you learned? What rules can you make? What questions do you have? On whiteboard.
20 min Board Meeting
PURPOSE: Reach consensus about equations that describe constant angular acceleration motion.
Review the kinematic representations in the basic 1-d constant acceleration model
Equations: d = Δpos, v = Δpos/Δt, a = Δv/Δt, d = v₀ + ½at², vf = v₀ + at
Velocity-time graph
When does this model apply? (when we have straight line motion)
What is the motion of the wheel? (not moving linearly, but it is moving)
Create a table of angular variables by analogy:
Linear Angular d = Δpos θ = Δangle v = Δpos/Δt ω = Δangle/Δt a = Δv/Δt α = Δω/Δt d = v₀t + ½at² θ = ω₀t + ½αt² vf = v₀ + at ωf = ω₀ + αt How to go between the two versions: d = rθ, v = rω, a = rα
Now add on the rest of relationships:
Linear Rotational m I = Σmᵢrᵢ² p = mv L = Iω Fnet = ma τ = Iα Ek = ½mv² Ekrot = ½Iω²
25 min Whiteboard - Helicopter Quantitative Problem (Word, Pdf)
PURPOSE: Model situation with constant angular acceleration
20 min Board Meeting
PURPOSE: Build consensus about modeling constant angular acceleration
Homework: Ranking of Theta vs t graph (Word, Pdf) and Rotational speed ranking (Word, Pdf)