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Phy 211: General Physics I

Explore the principles of motion in two and three dimensions, including displacement, velocity, and acceleration vectors. Learn about projectile motion and uniform circular motion. Lecture notes available.

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Phy 211: General Physics I

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  1. Phy 211: General Physics I Chapter 4: Motion in 2 & 3 Dimensions Lecture Notes

  2. rA(t0) v(t) 2-Dimensional Motion • A motion that is not along a straight line is a two- or three-dimensional motion. • The position, displacement, velocity and acceleration vectors are not necessarily along the same directions; the rules for vector addition and subtraction apply • The instantaneous velocity vector ( ) is always tangent to the trajectory but the average velocity () is always in the direction of • The instantaneous acceleration vector () is always tangent to the slope of the velocity at each instant in time but the average acceleration ( ) is always in the direction of rB(t1)

  3. Example of 2-D Motion

  4. Displacement, Velocity & Accelerations • When considering motion problems in 2-D, the definitions for the motion vectors described in Chapter 2 still apply. • However, it is useful to break problems into two 1-D problems, usually • Horizontal (x) • Vertical (y) • Displacement: • Velocity: • Acceleration: • Use basic trigonometry relations to obtain vertical & horizontal components for all vectors

  5. Horizontal: vx - vox = axt x - xo = ½ (vox + vx)t x - xo = voxt + ½ axt2 vx2 - vox2 = 2axDx Vertical: vy - voy = ayt y - yo = ½ (voy + vy)t y - yo = voyt + ½ ayt2 vy2 - voy2 = 2ayDy Equations of Kinematics in 2-D When to = 0 and a is constant: Remember: when to≠0, t replaces Dt in the above equations In Vector Notation:

  6. Projectile Motion Notes Projectile Motion is the classic 2-D motion problem: • Vertical motion is treated the same as free-fall • ay = - g = - 9.8 m/s2 {downward} • Horizontal motion is independent of vertical motion but connected by time but no acceleration vector in horizontal direction • ax = 0 m/s2 • As with Free Fall Motion, air resistance is neglected

  7. Projectile Motion Notes (cont.)

  8. r v Uniform Circular Motion • Object travels in a circular path • Radius of motion (r) is constant • Speed (v) is constant • Velocity changes as object continually changes direction • Since v is changing (v is not but direction is), the object must be accelerated: • The direction of the acceleration vector is always toward the center of the circular motion is referred to as the centripetal acceleration • The magnitude of centripetal acceleration:

  9. y v r y q x x Derivation of Centrifugal Acceleration Consider an object in uniform circular motion, where: r = constant {radius of travel} v = constant {speed of object} The magnitude of the centripetal acceleration ( ) can be obtained by applying the Pythagorean theorem: The components of the velocity vector continuous change as the objects travels around the circle and are related to the angle, q:

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