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Lecture 20

Lecture 20. Monday October 20. 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 Can no longer represent body by just a point.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.

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Lecture 20

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  1. Lecture 20 Monday October 20

  2. 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 Can no longer represent body by just a point.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.

  3. Uniform Rotation • ω = constant

  4. Rotation with angular acceleration • Non-uniform angular motion

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

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

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

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

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

  10. 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.

  11. Net Torque • If all forces are in the same plane

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