lecture07 - accelerations a r a to a r e of particles a to...

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Physics 131 Spring 2008 Dongping Zhong Lecture 7 (Monday, Apr. 7) Circular Motion Page 1 Angular variables
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Page 2 dt d t velocity angular average rad x rad rad rad r r length arc s r s radians circle full θ ω θ π π π θ θ = = = = = = 0 0 3 . 57 2 360 1 1 ) ( 2 2 , ) (
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Page 3 A particle moves cw around a circle at constant speed for 2.0 s. It then reverses direction and moves ccw at half the original speed until it has traveled through the same angle. Which is the particle’s angle-versus-time graph? (1) (2) (3) (4)
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Page 4 Circular Motion θ V v r ) / ( , ) cos sin ( ) ( ), sin (cos s rad dt d dt d j i r dt r d V t where j i r r θ ω θ θ θ θ θ θ θ = + = = = + = v v v v v v v Period: Time for 1 revolution (2 π ) ω π π ω 2 2 = = T T . r to is V v v ( rtz-coordinates )
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Page 5 r v a r a and r v r to opposite is a r j i r dt r d dt v d a j i v r v j i r s rad dt d dt d j i r dt r d v t r r t r V V V t t t 2 2 2 2 2 2 , ) sin cos ( 2 ) sin (cos ), cos sin ( ) / ( , ) cos sin ( = = = = = = = + = + = = + = = + = = ω ω ω θ θ ω π θ θ θ θ ω θ
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Unformatted text preview: accelerations ( a r ) a to ( a r ) e of particles a to e. 1. ( a r ) b > ( a r ) e > ( a r ) a > ( a r ) d > ( a r ) c 2. ( a r ) b = ( a r ) e > ( a r ) a = ( a r ) c > ( a r ) d 3. ( a r ) b > ( a r ) a = ( a r ) c = ( a r ) e > ( a r ) d 4. ( a r ) b > ( a r ) a = ( a r ) a > ( a r ) e > ( a r ) d 5. ( a r ) b > ( a r ) e > ( a r ) a = ( a r ) c > ( a r ) d Page 7 Relative Motion (reference frame) V PA =V PB +V BA Examples...
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