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# lecture5 - Kinematics in 2-D(II 2 Uniform circular motion r...

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1 Physics 1D03 - Lecture 5 Kinematics in 2 Kinematics in 2-D (II) D (II) • Uniform circular motion • Tangential and radial components of • Relative velocity and acceleration Serway and Jewett 4.4 to 4.6 a r Suggested Problems: Chapter 4 Problems 29, 31, 33, 37, 43 Physics 1D03 - Lecture 5 Uniform Circular Motion “uniform” means constant speed velocity changes (direction changes) acceleration : find by subtracting vectors, v r v r v r Δ t t Δ Δ = Δ v a r r 0 lim center 1 v r 2 v r 1 r r 2 r r 1) Is Δ v ∝ Δ t as Δ t 0 ? 2) What is the value of Δ v/ Δ t, as Δ t 0 ? Physics 1D03 - Lecture 5 Subtract velocities: θ Δ 1 v r 2 v r v r Δ Compare with displacements: 1 v r 2 v r 1 r r 2 r r Δ 1 r r 2 r r Δ r r Δ r r v v r r r r Δ = Δ Similar triangles, Note is perpendicular to v r Δ r r Δ Physics 1D03 - Lecture 5 From previous slide: r v r v r r Δ = Δ t t Δ Δ Δ Δ , v r v a r r r r as Δ t 0, 2 r v a = and so Direction: Since Δ v i s perpendicular to Δ r , a is perpendicular to v So, a is towards the centre of the circle (“centripetal”).

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lecture5 - Kinematics in 2-D(II 2 Uniform circular motion r...

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