lecture13 - Rotation (III) Rotation Torque and angular...

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Rotation (III) Rotation (III) Torque and angular acceleration “Moment of inertia” Text Sections : 10.7, and part of 10.4
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Angular velocity vector: parallel to the axis of rotation, following a similar right-hand rule: Angular acceleration vector: parallel to the angular velocity, if |ϖ| is increasing. ϖ rotation direction ϖ Force causes linear acceleration: F net = m a Torque causes angular acceleration: τ net = I α ?
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How much torque does it take to rotate a particular object? Better: How much torque does it take to change the rate of rotation ? What property of an object determines the response (angular acceleration) to an unbalanced external torque? Force causes linear acceleration: F net = m a Torque causes angular acceleration: τ net = I α ?
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The angular acceleration of a particle is proportional to the net torque applied to it. Example : A particle accelerates in a circle. Break the net force on it into radial and tangential components. Only F t causes tangential acceleration: F t F r r α τ∝ F t = ma t = m(r ) , since a t = r Multiply by r : rF t = mr 2 or torque = ( mr 2 )
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F ext f -f α r i m i For a rigid body, α is the same for all particles. The net force on each particle is composed of internal forces
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lecture13 - Rotation (III) Rotation Torque and angular...

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