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chapter7.4_7.5_slides

# chapter7.4_7.5_slides - v An object traveling in a circle...

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10/13/2009 1 An object traveling in a circle, even though it moves with a constant speed, will have an acceleration The centripetal acceleration is due to the change in the direction of the velocity Centripetal: “center - seeking”. It can be shown that the direction of the velocity changes points towards the center. Therefore the acceleration is directed toward the center of the circle of motion v v v t v v a i f For a constant speed circular motion, the magnitude of the centripetal acceleration is Do not confused the centripetal acceleration with the tangential acceleration a t we discussed earlier. Tangential acceleration is due to the change in the tangential speed. Centripetal acceleration is due to the change in the direction of the velocity r v a c 2 v v v r

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10/13/2009 2 Since the tangential speed is related to the angular speed by We have If the object is doing varying speed circular motion, then we have both tangential acceleration a t and centripetal acceleration a c , the magnitude of the total acceleration satisfies the Pythagorean theorem: r v 2 2 2 ) ( r r r r v a c 2 2 2 c t a a a 2 2 c t a a a c a t a a A discus thrower turns with an angular acceleration of . Find the total linear acceleration and the tangetial speed when he reaches an angular speed of 10 rad/s. Analysis: Total linear acceleration Solution: Find centripetal acceleration: Find the tangential acceleration 2 2 c t a a a 2 rad/s 50 m 8 . 0 2 2 2 m/s 80 10 8 . 0 r a c 2 m/s 40 50 8 . 0 r a t 2 2 2 m/s 89 80 40 a Tangential speed: m/s 8 8 . 0 10 r v t
10/13/2009 3

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chapter7.4_7.5_slides - v An object traveling in a circle...

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