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Published byImani Paley Modified about 1 year ago

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Monday October 20

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Motion of a rigid body Body can translate only. In this case we can replace the body by a point located at the center of mass. Body can rotate about a fixed point. Can no longer represent body by just a point. Body can translate and rotate. Rigid body means all points have the same angular velocity, ω, about the axis of rotation.

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Uniform Rotation ω = constant

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Rotation with angular acceleration Non-uniform angular motion

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Linear vs. Rotational Motion Linear variable Position x(t) Velocity Acceleration Circular variable Position θ(t) Velocity Acceleration

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Linear vs. Rotation Linear v constant a constant Rotation ω constant α constant

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Acceleration Two components: Centripetal, radially inward Tangential (rate at which particle’s velocity increases along the circular path)

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What corresponds to Force for rotational motion? Torque—twisting Which forces provides greater turning effectiveness to the bolt head? φ A B C

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Schematically Component of force perpendicular to lever arm (wrench handle) produces twist Longer wrench handle produces larger twist. φ r

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Torque, τ Torque, the measure of twist, is proportional to the length of the wrench handle, r, to the component of the applied force F perpendicular to the handle or lever arm.

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Net Torque If all forces are in the same plane

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