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Four Major Types of Two Dimensional Motion

Four Major Types of Two Dimensional Motion. 1. Projectile Motion 2. Circular Motion 3. Rotational Motion 4. Periodic Motion. Projectile motion problems are best solved by treating horizontal and vertical motion separately. * IMPORTANT * Gravity only affects vertical motion.

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Four Major Types of Two Dimensional Motion

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  1. Four Major Types of Two Dimensional Motion 1. Projectile Motion 2. Circular Motion 3. Rotational Motion 4. Periodic Motion

  2. Projectile motion problems are best solved by treating horizontal and vertical motion separately. *IMPORTANT* Gravity only affects vertical motion. There are two general types of projectile motion situations. 1. object launched horizontally 2. object launched at an angle

  3. Object Launched Horizontally vx = initial horizontal velocity h = initial height above ground t = total time in the air Rx = horizontal range IMPORTANT FACTS There is no horizontal acceleration. There is no initial vertical velocity. The horizontal velocity is constant. Time is the same for both vertical and horizontal. vertical horizontal Rx = vxt h = 0.5gt2

  4. Object Launched at an Angle v = initial velocity q = launch angle h = maximum height t = total time in air Rx = horizontal range IMPORTANT FACTS The horizontal velocity is constant. It rises and falls in equal time intervals. It reaches maximum height in half the total time. Gravity only effects the vertical motion. horizontal vx = v cosq Rx = vxt vertical vy = v sinq h = vyt/4 t = -2vy/g

  5. Learn more about projectile motion at these links: link1, link2, link3, link4, link5, link6 View projectile motion simulations at: link1, link2, link3, link4, link5, link6

  6. Suggested Constructivist Activities Students usesimulations tocomplete data tables and make graphs of the following situations: • constant initial velocity versus how the horizontal range changes with angle; plot “range vs angle” • constant initial velocity versus how total time in air changes with angle; plot “total time vs angle” • constant initial velocity versus how maximum height changes with angle; plot “height vs angle” • constant angle versus how the horizontal range changes with initial velocity; plot “range vs velocity” • constant angle versus how the total time in the air changes with initial velocity; plot “time vs velocity” • constant angle versus how the maximum height changes with initial velocity; plot “height vs velocity”

  7. object moves in circular path about an external point (“revolves”)

  8. According to Newton’s First Law of Motion, objects move in a straight line unless a force makes them turn. An external force is necessary to make an object follow a circular path. This force is called a CENTRIPETAL (“center seeking”) FORCE. Since every unbalanced force causes an object to accelerate in the direction of that force (Newton’s Second Law), a centripetal force causes a CENTRIPETAL ACCELERATION. This acceleration results from a change in direction, and does not imply a change in speed, although speed may also change.

  9. Centripetal force and acceleration may be caused by: • gravity - planets orbiting the sun • friction - car rounding a curve • a rope or cord - swinging a mass on a string In all cases, a mass m moves in a circular path of radius r with a linear speed v. The time to make one complete revolution is known as the period, T. The speed v is the circumference divided by the period. v r v = 2pr/T m

  10. The formula for centripetal acceleration is: ac= v2/r and centripetal force is: Fc=mac=mv2/r m = mass in kg v = linear velocity in m/s Fc = centripetal force in N r = radius of curvature in m ac = centripetal acceleration in m/s2

  11. Learn more about circular motion at these links: link1, link2, link3, link4, link5 View circular motion simulations at: link1, link2, link3, link4

  12. object moves in circular path about an internal point or axis (“rotates” or “spins”)

  13. The amount that an object rotates is its angular displacement. angular displacement, q, is given in degrees, radians, or rotations. 1 rotation = 360 deg = 2p radians The time rate change of an object’s angular displacementis its angular velocity. angular velocity,w, is given in deg/s, rad/s, rpm,etc...

  14. The time rate change of an object’s angular velocity is its angular acceleration. Angular acceleration, a, is given in deg/s2, rad/s2, rpm/s, etc... Formulas for rotational motion follow an exact parallel with linear motion formulas. The only difference is a change in variables and a slight change in their meanings.

  15. Constant LINEAR ROTATIONAL wf= wi + at vf = vi + at q = wavt d = vavt vav =(wf+ wi)/2 vav = (vf + vi)/2 q = wit+0.5at2 d = vit + 0.5at2 vf2 = vi2 + 2ad wf2= wi2+2aq

  16. P E R O D I C any motion in which the path of the object repeats itself in equal time intervals MOTION The simple pendulum is a great example of this type of motion.

  17. The period, T, of a simple pendulum (time needed for one complete cycle) is approximated by the equation: where l is the length of the pendulum and g is the acceleration of gravity.

  18. Learn more about pendulums and periodic motion at these links: link1, link2, link3, link4, link5 View pendulum simulations at: link1, link2, link3, link4, link5

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