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

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1 Physics 1D03 Rotation (III) Torque and angular acceleration “Moment of inertia” Text Sections : 10.7, and parts of 10.4, 10.5 Practice Problems: Chapter 10, Problems 25 a), 29, 30, 37, 39 Physics 1D03 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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2 Physics 1D03 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: α τ I = F t F r r F t = ma t = m(r α ) , since a t = r α Multiply by r : rF t = mr 2 α or torque = ( mr 2 ) α for a single particle: I=mass × (distance from rotation axis) 2 Physics 1D03 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
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