Lec08_Sum_f - Summary Lecture 8 Uniform circular motion: an...

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1 Lecture 8 Circular Motion: Examples Newton’s Law of Universal Gravitation Satellites Physics 111, Summer 2011, June 23, Lecture 8 Summary Speed in uniform circular motion: 2 Period (s) or frequency (Hz) of rotation: Uniform circular motion: an object moves on a circular path at constant speed. The magnitude of the force acting on the revolving object in the radial direction (radial or centripetal force): Radial (or centripetal) acceleration: The instantaneous velocity is tangential to the circle (perpendicular to the radius of the circle); acceleration is always perpendicular to the velocity vector and is called radial (or centripetal) acceleration. T f or f T 1 1 = = T r v π 2 = r v a R 2 = r v m F R 2 = Physics 111, Summer 2011, June 23, Lecture 8 Car Rounding a Banked Curve For a car moving around a banked curve it is possible to move at some speed when no friction is required. Find the banking angle if the speed is 15 m/s and the radius of a curve is 50 m. r v m F R 2 = r v m F F R N 2 sin = = θ 0 cos = mg F N cos mg F N = r v m mg 2 sin cos = r v g 2 cos sin = 46 . 0 ) / 8 . 9 )( 50 ( ) / 15 ( tan 2 2 2 = = = s m m s m rg v 3 0 0 1 25 66 . 24 46 . 0 tan = = r v g 2 tan = Physics 111, Summer 2011, June 23, Lecture 8 Vertical Circular Motion (#1) 4 mg F F T R + = 1 s m m s m gr v / 4 . 4 ) 2 )( / 8 . 9 ( 2 min 1 = = r v m F R 2 1 = A 0.2-kg ball on the end of a 2-m –long cord is swung in a vertical circle. Find the minimum speed the ball must have at the top of its arc so that the ball continues moving in a circle. mg F r v m T + = 1 2 1 mg r v m = min 2 1 0 (min) 1 = T F a) b) = = = g r v m mg r v m F T 2 1 2 1 1 Physics 111, Summer 2011, June 23, Lecture 8 R R F F =
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2 Vertical Circular Motion (#2) 5 mg F F T R = 2 r v m F R 2 2 = Find the tension in the cord at the point 2 if the speed of the ball is 4.4 m/s. mg r v m F T + = 2 2 2 N s m m s m kg g r v m mg r v m F T 9 . 3 ) / 8 . 9 ( 2 ) / 4 . 4 ( ) 2 . 0 ( 2 2 2 2 2 2 2 = + = + = + = mg F F R T + = 2 + = = + = g r v m mg r v m F T 2 2 2 2 2 Physics 111, Summer 2011, June 23, Lecture 8 1) 1.9 N
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This note was uploaded on 02/11/2012 for the course PHYSICS 111 taught by Professor B during the Summer '08 term at Iowa State.

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Lec08_Sum_f - Summary Lecture 8 Uniform circular motion: an...

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