Physics 121 11/3/10 Prof. E. F. Redish 1 11/3/10 1 Physics 121 11/3/10 2 Physics 121 7.1 7.2 7.3 a 31% 67% 0% b 1% 10% 1% c 28% 1% 1% d 77% 5% 72% e 19% 10% 24% f 2% 11/3/10 3 Physics 121Physics 121 11/3/10 Prof. E. F. Redish 2 11/3/10 8 Physics 121 R R v t v v a t Similar triangles imply RvaRvvavtaRtv2===11/3/10 9 Physics 121 rRvarRrrRvaˆectorposition v ofdirection in r unit vecto ˆectorposition v center in to pointing 22=====11/3/10 10 Physics 121Physics 121 11/3/10 Prof. E. F. Redish 3 11/3/10 11 Physics 121 rRmvFrRvmFrRvamFanetnetnetˆˆ ˆ 222====always in order for the object to move in a circle with constant speed. Therefore, to do this, we need a net force. A(n inward) radial net force is needed to maintain circular motion. 11/3/10 12 Physics 121 R Position Velocity Acceleration R R v t v v a t RvaRvvavtaRtv2 ===11/3/10 13 Physics 121 x y tt === degrees)(in 3602 radians)(in t=0 Uniform motion:Physics 121 11/3/10 Prof. E. F. Redish 4 11/3/10 14 Physics 121 )()(0000000tttttto+===== 11/3/10 15 Physics 121 x y )(ˆ)sin(ˆ)cos(ˆˆ000ttjRiRjyixr+=+=+= What happens as t (and ) gets large (bigger than 2)? 11/3/10 16 Physics 121 -1.5-1-0.500.511.50 5 10 15 20 25thetasin(theta)-1.5-1-0.500.511.50 5 10 15 20 25thetacos(theta)Physics 121 11/3/10 Prof. E. F. Redish 5 11/3/10 25 Physics 121 R x y x = Rcosy = Rsinddsin= cosddcos= sinUniform motion: =0t with 0= constantdd0t()=10ddtddsin=1 0ddtsin 0t()= cos tddcos=1 0ddtcos 0t()= sin tddtsin 0t()= 0cos 0tddtcos 0t()= 0sin 0t11/3/10 26 Physics 121 R x y x = Rcosy = Rsinvx=dxdt= Rddtcos= 0Rsin= 0yvy=dydt= Rddtsin= 0Rcos= 0xax=dvxdt= 0Rddtsin= 02Rcos= 02xay=dvydt= 0Rddtcos= 02Rsin= 02yNow figure out what all that
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