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Chapter 07a - Chapter 7A Chapters 7 and 8 deal with...

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Chapter 7A 1 Chapters 7 and 8 deal with rotational motion, and with objects traveling in circular paths.
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Chapter 7A 2 Angular Displacement ( θ ) An object’s angular displacement ( θ ) is the angle through which it rotates during some time interval. The positive direction is counterclockwise . Angular displacements can be expressed in degrees, radians, or revolutions. θ time = t f time = t i
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Chapter 7A 3 Expressing Angles in Radians 1 rev. = 360° = 2 π radians 1 radian 57.3° An angle in radians is a “pure number” - the length units cancel. “Radian” labels will appear and disappear in calculations. θ = s r = arc length radius θ s r
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Chapter 7A 4 Angular Speed ( ϖ ) ϖ = ϖ av = θ t ϖ = lim t 0 θ t Units for ϖ : radians / second Counterclockwise rotation is positive. An object’s angular speed ( ϖ ) tells us how rapidly its angular displacement ( θ ) is changing (how rapidly it is spinning): θ time = t f time = t i
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Chapter 7A 5 Angular Acceleration ( α ) Units for α : radians / second 2 The angular acceleration ( α ) will have the same sign as the angular speed ( ϖ ) if the object is speeding up, and the opposite sign if it is slowing down. α = α av = ϖ t α = lim t 0 ϖ t If an object’s angular speed ( ϖ ) is changing, it is undergoing angular acceleration ( α ): ϖ 0 ϖ 1 ϖ 2 ϖ 3 ϖ 4 ϖ 5 ϖ 7 ϖ 6
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Chapter 7A 6 Summary The angular variables describe the rotational motion of an object as a whole.
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