Radians and Degrees

  • In degrees, once around a circle is 360°

  • In radians, once around a circle is 2π

  • A radian measures a distance around an arc equal to the length of the arc's radius

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Linear vs. Angular Displacement


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Linear vs. Angular Velocity


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Direction of Angular Velocity

L = 10) irection of rotati Right hand Direction of rotation

Converting Linear to Angular Velocity


Linear vs. Angular Acceleration


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Centripetal Acceleration

Express position vector in terms of unit vectors. Fte)z r$in a —Jr sin

Reference Frames

  • A reference frame describes the motion of an observer

    • Most common reference frame is Earth
  • Laws of physics we study in this course assume we're in an inertial, non-accelerating reference frame

  • There is no way to distinguish between motion at rest and motion at a constant velocity in an inertial reference frame

Calculating Relative Velocities

  • Consider two objects, A and B.

  • Calculating the velocity of A with respect of reference frame B (and vice versa) is straightforward

  • Example:

    • Speed of car with respect to the ground

    • Walking on a train, speed of a person with respect to the train

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Linear vs. Angular

Rotational Motion (a = constant) 0=00 -Fat = — (00 + e = + —at2 02 = + 2a9 Linear Motion (a = constant) v vo + at vot + —at 2 2 = v: + 2ax

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