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Fundamentals of Mechanics: Straight-line Motion & Circular Motion Principles

Learn about straight-line motion with constant acceleration, freely falling bodies, projectile motion, and uniform circular motion. Understand concepts like average velocity, instantaneous velocity, and acceleration. Dive into detailed examples and calculations to enhance your understanding.

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Fundamentals of Mechanics: Straight-line Motion & Circular Motion Principles

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  1. Chapter IIMechanics • Streight-line motion, average and instantaneous x-velocity • Streight-line motion with constant acceleration • Freely falling bodies • Projectile motion • Uniform Circular motion

  2. A. Streight-line motion, average and instantaneous x-velocity 1. Average Velocity s = distance y r = displacement A t1 s The displacement of a particle is defined as its change in position. r1 r B r2 t2 0 x Magnitude of Average velocity Average Speed

  3. The averagespeed of a particle, a scalar quantity, is defined as the total distance traveled divided by the total time it takes to travel that distance • The average velocity of a particle is defined as the particle’s displacement r divided bythe time interval t during which that displacement occurred

  4. 2. Instantaneous Velocity Instantaneous velocity v equals the limiting value of the ratio r/t as t approaches zero Magnitude of Instantaneous velocity = Instantaneous Speed The instantaneous speed of a particle is defined as the magnitude of its velocity 3. Acceleration The average acceleration of the particle is defined as the change in velocity v divided by the time interval t

  5. B. Streight-line motion with constant acceleration

  6. C. Freely Falling Bodies reference y = -h yo = 0 vo = 0 = - g • - h = 0 + 0 t + ½(- g) t2 • h = - ½ g t2 • h = ½ g t2 h For example, look exercise number 2.44 at page 87 (66)

  7. A hot-air balloonist, rising vertically with a constant velocity of magnitude 5.00 m/s, releases a sandbag at an instant when the balloon is 40.0 m above the ground. Afterit is released, the sandbag is in free fall. (b) How many seconds after its release will the bag strike the ground?

  8. D. Projectile motion y vox = vo cos α voy = vo sin α y-direction v = voy + at = vo sin α + at y = voy t + ½ a t2 = vo t sin α + ½ a t2 x-direction v = vox = vo cos α x = vox t = vo t cos α vo voy α 0 x vox

  9. v2  v R v2 v1 v1 r2 E. Uniform Circular Motion r1 r2  r as r1 R = circular radius as = centripetal acceleration t = time interval

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