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Angular Kinematics

Angular Kinematics. Linear kinematics does not handle curving trajectories well Always have acceleration due to changing direction Need to know radius of turn Want to isolate the motion of curving trajectories. A straight line has an always changing “radius” from a single point.

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Angular Kinematics

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  1. Angular Kinematics • Linear kinematics does not handle curving trajectories well • Always have acceleration due to changing direction • Need to know radius of turn • Want to isolate the motion of curving trajectories

  2. A straight line has an always changing “radius” from a single point • Can think of “rolling up” a line so the radius is constant

  3. Definition of angular quantities • Angle corresponds to displacement • q = x / r • x is distance along curve, r is radius of curve • Angular velocity corresponds to velocity • w = Dq/Dt = v / r • Angular acceleration corresponds to tangential acceleration • a = Dw/Dt = at / r • at generates a speed change, not a directional change

  4. Note that these are simply the linear quantities divided by the radius! • Can we use this to find kinematic relationships? • This is the displacement equation for angular motion!

  5. Can derive other kinematic equations in a same way • Notice that linear kinematic equation and angular kinematic equation are almost the same • Replace linear quantities with angular quantities to transform between them

  6. Direction of angular motion • Angular motion, like all motion, has a direction • Only stationary point is the center of the circle • Center defines axis of rotation • Use right hand rule to define direction • Curl fingers of right hand in direction of spin • Thumb points in direction of motion

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