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Rotational Kinematics and Energy

Rotational Kinematics and Energy
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Dr.SamuelHunt,United Arab Emirates,Teacher
Published Date:21-07-2017
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Chapter 10 Rotational Kinematics and EnergyUnits of Chapter 10 • Angular Position, Velocity, and Acceleration • Rotational Kinematics • Connections Between Linear and Rotational Quantities •Rolling Motion • Rotational Kinetic Energy and the Moment of Inertia • Conservation of Energy (Not required)10-1 Angular Position, Velocity, and Acceleration10-1 Angular Position, Velocity, and Acceleration Degrees and revolutions:10-1 Angular Position, Velocity, and Acceleration Arc length s, measured in radians:10-1 Angular Position, Velocity, and Acceleration10-1 Angular Position, Velocity, and Acceleration10-1 Angular Position, Velocity, and Acceleration10-1 Angular Position, Velocity, and Acceleration10-2 Rotational Kinematics If the angular acceleration is constant:10-2 Rotational Kinematics Analogies between linear and rotational kinematics:10-3 Connections Between Linear and Rotational Quantities10-3 Connections Between Linear and Rotational Quantities10-3 Connections Between Linear and Rotational Quantities10-3 Connections Between Linear and Rotational Quantities This merry-go-round has both tangential and centripetal acceleration.10-4 Rolling Motion If a round object rolls without slipping, there is a fixed relationship between the translational and rotational speeds:10-4 Rolling Motion We may also consider rolling motion to be a combination of pure rotational and pure translational motion:10-5 Rotational Kinetic Energy and the Moment of Inertia For this mass,10-5 Rotational Kinetic Energy and the Moment of Inertia We can also write the kinetic energy as Where I, the moment of inertia, is given by Use this equation to calculate I, for a few point masses. 10-5 Rotational Kinetic Energy and the Moment of Inertia Moments of inertia of various regular shapes can be calculated using these known results: