How do we describe angular momentum?

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Presentation transcript:

How do we describe angular momentum? HW:

What affects an objects rotational inertia? The axis of rotation The distribution of mass For many objects the mass is continuously distributed, which makes calculating “I” a pain. Hoop: I = mr2 Cylinder: I = (1/2)mr2

Uhhh oh, do I have to memorize??? NO! There are many different expressions for rotational inertia (8 in your textbook), but usually they will be given or are intuitive. When figuring out “I” is complicated, you may be able to solve for it in other ways, by using the second law: I = Στ/α Common AP question: “Ranking Task”

How is angular momentum represented? In order to answer this question we need to ask ourselves how linear momentum is represented. Linear Mom. p = mv J = F x t = Δp Rotational Mom. L = Iω ΔL = Στ x Δt Symbol: L SI Units: kg.m2/s

Conservation of Angular Momentum Without an acceleration can there be a force? Without an angular acceleration can there be a torque? If there is no torque on an object, will the angular momentum change? Similar to the linear case, without a change in torque or angular velocity there can not be a change in “angular momentum”. It remains constant! Iω = I’ω’ = constant

Angular Mom. Demo How is angular momentum conserved? What factors are changing to conserve momentum? Once spinning is any additional torque or angular acceleration provided?

Practice Angular Mom. Iω = I’ω’ Mr2ω = (Mr2)’ω’ Astronauts use a centrifuge to simulate the harshness of a shuttle launch. Initially the centrifuge has a length of 8m and an angular velocity of 10 rad/sec. The machine is then pulled in to half it’s length while spinning. What is the new angular velocity? Iω = I’ω’ Mr2ω = (Mr2)’ω’ M.640(rad.m/s) = M.16m.ω’ 640 (rad.m/s) = 16m.ω’ ω’ = 40 rad/sec

Summary Why is the equation for rotational inertia not always the same? What is the equation for angular momentum? How is angular momentum conserved?