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CHAPTER 3 MOTION IN A PLANE

Learn how position vectors, velocity vectors, and projectile motion are used to describe and analyze the motion of objects in a plane. Explore the principles of independence of horizontal and vertical motions, constant-acceleration equations, and uniform circular motion.

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CHAPTER 3 MOTION IN A PLANE

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  1. CHAPTER 3 MOTION IN A PLANE

  2. Position vectors can specify the location and displacement of a point in an x-y coordinate system

  3. Velocity In A Plane vav = (r2-r1) / (t2–t1) = Δr / Δt Components of the average velocity vectors are: vav,x= Δx / Δt and vav,y= Δy / Δt

  4. At every point along the path, the instantaneous velocity vector is tangent to the path.

  5. Independence Of Horizontal And Vertical Motions

  6. PROJECTILE MOTION A projectile is any object that is given an initial velocity and then follows a path determined entirely by the effects of gravitational acceleration and air resistance. In studying projectile motion we make the following assumptions: Air resistance is ignored. The acceleration of gravity is constant, downward, and has a magnitude equal to g = 9.81 m/s2. The Earth’s rotation is ignored. The Earth’s curvature is ignored.

  7. Constant-Acceleration Equations of Motion in Two-Dimensions

  8. Determination of key itemsfor projectiles • x = (vocos o)t •  = tan-1(vy/vx) • y = (vosin o)t - ½gt2 • vx = vocoso • vy = vosino- gt

  9. UNIFORM CIRCULAR MOTION

  10. Uniform Circular Motion

  11. Centripetal Acceleration arad = v2/R

  12. HOMEWORK: • 12, 17,22,36,

  13. A daring 510 N swimmer dives off a cliff with a running horizontal leap, as shown in the figure below.   What must her minimum speed be just as she leaves the top of the cliff so that she will miss the ledge at the bottom, which is 1.75 m wide and 9.00 m below the top of the cliff?

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