Warm-up (9/26/18) How does one calculate linear momentum? What is the law of conservation of linear momentum? What would you predict is the rotational motion analog to these linear motion concepts (momentum and its conservation)

Angular Momentum Reference Page: 555

Angular Momentum (L) 𝐿=𝐼𝜔 Rotational equivalent of linear momentum. Product of a body’s moment of inertia and its angular velocity Vector quantity (use right-hand rule: curve fingers in direction of rotation, thumb points in vector direction of L) 𝐿=𝐼𝜔

Angular Momentum (L) What should the units for Angular Momentum be? 𝒌𝒈∙ 𝒎 𝟐 ∙𝐫𝐚𝐝∙ 𝒔 −𝟏

Question 8.12 Spinning Bicycle Wheel You are holding a vertically-spinning bicycle wheel while standing on a stationary turntable. If you suddenly flip the wheel 90° so that it is spinning horizontally, the turntable will: a) remain stationary b) start to spin in the opposite direction as the wheel c) start to spin in the same direction as the wheel Answer: b

Question 8.12 Spinning Bicycle Wheel You are holding a vertically-spinning bicycle wheel while standing on a stationary turntable. If you suddenly flip the wheel 90° so that it is spinning horizontally, the turntable will: a) remain stationary b) start to spin in the opposite direction as the wheel c) start to spin in the same direction as the wheel

Conservation of Angular Momentum Rotational equivalent of the conservation of linear momentum Given no outside forces, the total angular momentum of a system will remain constant, even if there are internal changes (i.e. to the moment of inertia of the system) Examples: Divers; figure skaters; gymnasts; drills in space

Example… What happens as you bring your arms in and hug yourself as you are spinning on the stool? WHY? Ice Skaters experience the same phenomenon…. What’s happening?

Warm-up: 9/27/18 If the Earth were to magically expand, doubling its radius while keeping its mass the same, would the length of the day increase, decrease, or stay the same? EXPLAIN your reasoning.

Sample Problem 1 A 0.0150 kg record with a radius of 15.0 cm rotates with an angular speed of 3.49 rad·s-1. What is the angular momentum of the record?

Sample Problem 2 For a classroom demonstration, Alec sits on a rotating stool and holds weights in each hand. Initially he holds his arms outstretched (I=5.33 kg·m2) and spins on the stool with an angular speed of 3.74 rad ·s-1. While spinning, he pulls his arms in to his chest, reducing the moment of inertia to 1.60 kg·m2. What is his new angular speed? What moment of inertia would be required to give a final angular speed of 10.0 rad·s-1 ?

Sample Problem 3 A star of radius R=2.30 x 108 m rotates with an angular speed of 2.40 x 10-6 rad·s-1. If this star then collapses down to a radius of 20.0 km, what is its final angular speed? Assume the star is a uniform sphere (𝐼= 2 5 𝑀 𝑅 2 ) At what radius will the star have a period of rotation equal to 15.0 ms?