L08 - Physics 111 Lecture 8 "The pursuit of perfection...

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1 / 13 Physics 111 Lecture 8 “The pursuit of perfection often impedes improvement.” –George F. Will
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Angle Angle “Units” of angles Rotational variables Question Example Relating variables Example Question 2 / 13 Many things (e.g., doors that are being opened, planets) don’t move in linear paths A convenient way to describe such motion is by means of angular variables Angle : Figure formed by two rays sharing a common endpoint Magnitude: “amount of rotation” that separates both rays ( k ) θ = s 1 r 1 = s 2 r 2 (1) Angles are dimensionless , since they are de±ned as the ratio of two lengths Sign: Counterclockwise is positive, clockwise is negative
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“Units” of angles Angle “Units” of angles Rotational variables Question Example Relating variables Example Question 3 / 13 Radian : Angle subtended by an arc of a circle that has the same length as the circle’s radius θ = s r (2) Example : One circle is 2 π radians, half a circle has π radians, and so on Degree : 1 / 360 of a full circle θ o = 360 o 2 π radians s r (3) Conversion factor: 360 o = 2 π radians 90 o = π 2 radians , 180 o = π radians Common angles have easy numbers in degrees, but Eq. (2) is valid only if we use radians
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Rotational variables Angle “Units” of angles Rotational variables Question Example Relating variables Example Question 4 / 13 Angular displacement : Change in angular position Δ θ = θ f - θ i (4) For ease, when dealing with angular displacement, we say that we are dealing with a rigid body
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L08 - Physics 111 Lecture 8 "The pursuit of perfection...

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