AP Physics 1 - Rotational Motion and Angular Momentum

AP Physics 1 - Rotational Motion and Angular Momentum

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Section 1

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Rotational kinetic energy KE(rot)

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Cards (36)

Section 1

(36 cards)

Rotational kinetic energy KE(rot)

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Back

**Rotational Kinetic Energy: Work and Energy Revisited

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What is linear or tangential acceleration?

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Linear or tangential acceleration, 𝑎𝑡 refers to changes in the magnitude of velocity but not its direction. In circular motion centripetal acceleration, 𝑎𝑐 , refers to changes in the direction of the velocity but not its magnitude.

Back

What is angular acceleration?

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Uniform circular motion: motion in a circular path at constant speed

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What is the relationship between force, mass, radius and angular acceleration?

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To develop the precise relationship among force, mass, radius, and angular acceleration, consider what happens if we exert a force F on a point mass m that is at a distance r from a pivot point

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**Kinematics of Rotational Motion

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What is the equation that shows this relationship?

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This equation is the rotational analog of Newton's second law (F=ma ) Torque is analogous to force Angular acceleration is analogous to translational acceleration mr^2 is analogous to mass (or inertia)

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Example: A deep-sea fisherman hooks a big fish that pulls line from his fishing reel, which is initially at rest. The reel is given an angular acceleration of 110 𝑟𝑎𝑑/𝑠2 for 2.00 𝑠 and line unwinds from the reel at a radius of 4.50 cm from its axis of rotation. (a) What is the final angular velocity of the reel?

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Example: A powerful motorcycle can accelerate from 0 to 30.0 m/s in 4.20 s. What is the angular acceleration of its 0.320 m radius wheels?

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What occurs with angular acceleration when change occurs?

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There is an angular acceleration, in which 𝜔 changes. The faster the change occurs, the greater the angular acceleration. -where delta omega is the change in angular velocity and delta t is the change in time. The units of angular acceleration are rad/s2.

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Example of Conservation of angular momentum

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What happens to angular momentum when net torque is zero?

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What is kinematics? What is kinematics of rotational motion?

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Kinematics is the description of motion. The kinematics of rotational motion describes the relationships among rotation angle, angular velocity, angular acceleration, and time.

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Main idea of rotational inertia

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(b) At what speed is fishing line leaving the reel after 2.00 s elapses?

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How is angular momentum defined?

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We define angular momentum L as L = Iw As we would expect, an object that has a large moment of inertia I, such as Earth, has a very large angular momentum.

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What happens if omega increases or decreases? What is the angular acceleration (alpha)?

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What is the equation for torque, moment of intertia, and angular acceleration?

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The units of moment of intertia are kgm^2 (If you want to give something angular acceleration - you need torque).

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(c) How many revolutions does the reel make?

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Rotational and Translational Quantities

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Example: Suppose an ice skater is spinning at 0.800 𝑟𝑒𝑣/ 𝑠 with her arms extended. She has a moment of inertia of 2.34𝑘𝑔 ⋅ 𝑚2 with her arms extended and of 0.363𝑘𝑔 ⋅ 𝑚2 withherarmsclosetoherbody.(a)Whatisherangularvelocityinrevolutionsper second after she pulls in her arms? (b) What is her rotational kinetic energy before and after she does this?

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net work (W) = net Fd cos(theta)

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Tangential acceleration is directly related to?

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Tangential acceleration alpha t is directly related to the angular acceleration alpha and is linked to an increase or decrease in the velocity, but not its direction.

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**Angular Momentum and Its Conservation

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Example: A father pushing a playground merry-go-round. He exerts a force of 250 𝑁 at the edge of the 50.0 𝑘𝑔 merry-go-round, which has a 1.50 𝑚 radius. Calculate the angular acceleration produced when no one is on the merry-go-round. Consider the merry-go-round itself to be a uniform disk.

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**Conservation of angular momentum

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How do we define angular velocity (omega)?

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We defined angular velocity 𝜔 as the time rate of change of an angle theta.

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**Moment of Inertia and Torque

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Rotational Inertia

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Kinematics of Rotational Motion

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Example: Suppose a teenager puts her bicycle on its back and starts the rear wheel spinning from rest to a final angular velocity of 250 rpm in 5.00 s. (a) Calculate the angular acceleration in rad/s2. (b) If she now slams on the brakes, causing an angular acceleration of -87.3rad/s2 , how long does it take the wheel to stop?

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What is the equation for the law of conservation of angular momentum?

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Work energy theorem for rotational motion only

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**Dynamics of Rotational Motion: Rotational Inertia

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What is the relationship between tangential acceleration a(t) and angular accretion (alpha)?

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**Tangential acceleration and centripetal acceleration

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