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Unformatted text preview: Motion in Two Dimensions Chapter 4 2 Dimensional Motion We will consider motion the the xy plane. Positions now have (x,y) coordinates, so we need to use vectors. There are two types of problems we need to consider Throw or drop an object at an angle to the horizontal Make something go around in a circle Positions are VECTOR Quantities r r r r r r ∆ = = ∆ + φ ι φ ι ∆ r = r f r i = x f x i ( ) ö i + y f y i ( ) ö j + z f z i ( ) ö k Note: ∆ r is not necessarily the length of the path traversed by the particle. Average Velocity The average velocity of a particle during a time interval ∆t is the displacement of the particle divided by the time interval: v ≡ ∆ρ ∆τ The average velocity between two points is independent of the path taken . Instantaneous Velocity The instantaneous velocity is the limit of the average velocity as the time interval ∆t approaches zero: v ≡ λιμ ∆ τ → 0 ∆ρ ∆τ = δρ δτ The magnitude of the instantaneous velocity is the speed . r can change in magnitude, direction, or both. Average Acceleration The velocity can also change. The average acceleration is the rate at which v changes over an interval: a ≡ ∆ω ∆τ v i + ∆ω= ω φ ω ι ω φ = ∆ω a can change in magnitude, direction, or both. CPS Question 2 Dimensional Motion Let’s consider 2D motion during which the acceleration remains constant in both magnitude and direction. r = ξ ι + ψ ϕ v = δρ δτ = δξ δτ ι + δψ δτ ϕ= ω ξ ι + ω ψ ϕ Because a is constant, it’s components a x and a y are also constant. Therefore, v f = ω ξι + α ξ τ ( 29 ι + ω ψι + α ψ τ ( 29 ϕ = ω ξι ι + ω ψι ϕ ( 29 + α ξ ι + α ψ ϕ ( 29 τ = ω ι + ατ...
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 Summer '08
 bose
 Physics, Acceleration, Power, Velocity, Ri

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