# 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.

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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 Can no longer represent body by just a point.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. Rigid body means all points have the same angular velocity, ω, about the axis of rotation.

Uniform Rotation ω = constant

Rotation with angular acceleration Non-uniform angular motion

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

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

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

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

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

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.

Net Torque If all forces are in the same plane

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