Kinematics II

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Kinematics II. Week 2. Contents. Radians Uniform Circular Motion Projectile Motion Summary of Kinematics I & II. A radian is a measure of an angle. Radius = 1 Ө = arc length 360˚ = 2 π radians 180 ˚ = π radians. Radians. arc. Ө. Unit Circle; radius = 1. Quiz 1. - PowerPoint PPT Presentation

Transcript of Kinematics II

  • Kinematics IIWeek 2

  • ContentsRadiansUniform Circular MotionProjectile MotionSummary of Kinematics I & II

  • RadiansA radian is a measure of an angle.Radius = 1 = arc length

    360 = 2 radians180 = radiansUnit Circle; radius = 1arc

  • Quiz 1Which of the following radian measures is equivalent to 90?

    2/2/3/4

  • Quiz 1Which of the following radian measures is equivalent to 90?

    180 = radians90 = /2 radians

    ANSWER: /2

  • Arc LengthWhen radius = 1arc = When radius = rarc = r

    * must be in radiansarcr

  • Uniform Circular MotionUniform implies constant speed while moving in a circle

    Angular Frequency = /sec

  • Quiz 2An object in circular motion moves 180 per second has an angular frequency of what?23/2/2/3/4

  • Quiz 2An object in circular motion moves 180 per second has an angular frequency of what?

    ANSWER: = /2 radians/sec

  • Angular Speedarc = r = /sec

    Angular speed:v= arc/sec= (r)/sec= r(/sec)= r

  • Summary = arc length (r=1)arc = r = /secv = arc/sec = r

    rarc

  • Quiz 3An object in circular motion travels at 3 radians/sec in a circle of radius 5m. What is its angular speed?3/5 m/sec5/3 m/sec2 m/sec8 m/sec15 m/sec

  • Quiz 3An object in circular motion travels at 3 radians/sec in a circle of radius 5m. What is its angular speed?

    = 3 radians/secv = rv = (5)(3) = 15 m/sec

    ANSWER: 15 m/sec

  • Centripital ForceAn object travelling in circular motion experiences a centripetal force FThe induced acceleration isa = v2/rF

  • Quiz 4Imagine that the centripetal force applied on an object moving in circular motion is suddenly shut off. What would happen?The object spirals outwardsThe object spirals inwardsThe object continues to move in uniform circular motionThe object decelerates while continuing to move in a circleThe object moves away in a straight line

  • Quiz 4Imagine that the centripetal force applied on an object moving in circular motion is suddenly shut off. What would happen?

    ANSWER: The object moves away in a straight line (Newtons first law)

  • Projectile MotionAn object experiences gravitational acceleration g=9.80m/s2 downwards as it moves

  • Projectile MotionProjectile motion is really two independent 1-D motionsOne in the x directionOne in the y direction

  • x-directionThe x-direction experiences NO acceleration, thus

    x = vxt

    (Its that simple!)

  • y-directionThe y-direction experiences an acceleration downwards, thus

    y = vyt gt2

  • Velocity Componentsx = vxty = vyt gt2vvxvyvx = v cosvy = v sin

  • Quiz 5At what angle should a cannon be positioned so that the projectile travels the farthest?906045300

  • Quiz 5At what angle should a cannon be positioned so that the projectile travels the farthest?

    ANSWER: 45

  • Proof of Quiz 5x = vxty = vyt gt2vx = v cosvy = v sin

    Let y = 0 t = 2vy/g x = 2vxvy/g x = (2v2 sin cos)/g x = (v2 sin2)/g xmax = v2/g when 2 = 90 = 45

    y = 0y = 0* Trig. Identity:sin2 = 2sin cos

  • Review Linear Motion under Uniform Accelerationx = x0 + v0t + at2v = v0 + atx = vavet = [(v0 + v)/2]tv2 - v02 = 2ax

    Uniform Circular Motion = arc length (r=1)arc = r = /secv = arc/sec = ra = v2/r

    Projectile Motionx = vxty = vyt gt2vx = v cosvy = v sin

  • Next WeekChoice 1Review kinematicsChoice 2Newtons laws

  • The End